
<PAGE>   1
 
                                                                    EXHIBIT 25.1
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
 
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                             ---------------------
                                    FORM T-1
 
                            STATEMENT OF ELIGIBILITY
                   UNDER THE TRUST INDENTURE ACT OF 1939 OF A
                    CORPORATION DESIGNATED TO ACT AS TRUSTEE
 
                  [ ] CHECK IF AN APPLICATION TO DETERMINE
                      ELIGIBILITY OF A TRUSTEE PURSUANT TO
                               SECTION 305(b)(2)
                             ---------------------
 
                       IBJ SCHRODER BANK & TRUST COMPANY
              (Exact name of trustee as specified in its charter)
 
<TABLE>
<S>                                            <C>
                   NEW YORK                                      13-6022258
        (Jurisdiction of incorporation                        (I.R.S. employer
 or organization if not a U.S. national bank)               identification No.)
     ONE STATE STREET, NEW YORK, NEW YORK                          10004
   (Address of principal executive offices)                      (Zip code)
</TABLE>
 
                      LUIS PEREZ, ASSISTANT VICE PRESIDENT
                       IBJ SCHRODER BANK & TRUST COMPANY
                                ONE STATE STREET
                            NEW YORK, NEW YORK 10004
                                 (212) 858-2000
 
           (Name, address and telephone number of agent for service)
 
                              RENTERS CHOICE, INC.
                              RENT-A-CENTER, INC.
                                COLORTYME, INC.
              (Exact names of obligor as specified in its charter)
 
<TABLE>
<S>                                            <C>
                   DELAWARE                                      48-1024367
                   DELAWARE                                      48-0959188
                    TEXAS                                        75-2651408
       (State or other jurisdiction of                        (I.R.S. employer
        incorporation or organization)                      identification No.)
             RENTERS CHOICE, INC.
       13800 MONTFORT DRIVE, SUITE 300
                DALLAS, TEXAS                                      75240
             RENT-A-CENTER, INC.
            8200 EAST THORN DRIVE
               WICHITA, KANSAS                                     67226
               COLORTYME, INC.
        1231 GREENWAY DRIVE, SUITE 900
                IRVING, TEXAS                                      75038
   (Address of principal executive offices)                      (Zip code)
</TABLE>
 
                     11% SENIOR SUBORDINATED NOTES DUE 2008
                        (Title of indenture securities)
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
<PAGE>   2
 
ITEM 1. GENERAL INFORMATION
 
Furnish the following information as to the trustee:
 
     (a) Name and address of each examining or supervising authority to which it
     is subject.
 
       New York State Banking Department
       Two Rector Street
       New York, New York
 
       Federal Deposit Insurance Corporation
       Washington, D.C.
 
       Federal Reserve Bank of New York
       Second District,
       33 Liberty Street
       New York, New York
 
     (b) Whether it is authorized to exercise corporate trust powers.
 
        Yes
 
ITEM 2. AFFILIATIONS WITH THE OBLIGOR.
 
If the obligor is an affiliate of the trustee, describe each such affiliation.
 
The obligor is not an affiliate of the trustee.
 
ITEM 13. DEFAULTS BY THE OBLIGOR.
 
     (a) State whether there is or has been a default with respect to the
     securities under this indenture. Explain the nature of any such default.
 
        None
 
     (b) If the trustee is a trustee under another indenture under which any
     other securities, or certificates of interest or participation in any other
     securities, of the obligors are outstanding, or is trustee for more than
     one outstanding series of securities under the indenture, state whether
     there has been a default under any such indenture or series, identify the
     indenture or series affected, and explain the nature of any such default.
 
        None
 
ITEM 16. LIST OF EXHIBITS.
 
List below all exhibits filed as part of this statement of eligibility.
 
     *1. A copy of the Charter of IBJ Schroder Bank & Trust Company as amended
     to date. (See Exhibit I A to Form T-1, Securities and Exchange Commission
     File No. 22-18460).
 
                                        2
<PAGE>   3
 
     *2. A copy of the Certificate of Authority of the trustee to Commence
     Business (Included in Exhibit 1 above).
 
     *3. A copy of the Authorization of the trustee to exercise corporate trust
     powers, as amended to date (See Exhibit 4 to Form T-1, Securities and
     Exchange Commission File No. 22-19146).
 
     *4. A copy of the existing By-Laws of the trustee, as amended to date (See
     Exhibit 4 to Form T-1, Securities and Exchange Commission File No.
     22-19146).
 
     5. Not Applicable
 
     6. The consent of United States institutional trustee required by Section
     321(b) of the Act.
 
     7. A copy of the latest report of condition of the trustee published
     pursuant to law or the requirements of its supervising or examining
     authority.
-------------------------
 
* The Exhibits thus designated are incorporated herein by reference as exhibits
  hereto. Following the description of such Exhibits is a reference to the copy
  of the Exhibit heretofore filed with the Securities and Exchange Commission,
  to which there have been no amendments or changes.
 
                                        3
<PAGE>   4
 
                                      NOTE
 
In answering any item in this Statement of Eligibility which relates to matters
peculiarly within the knowledge of the obligor and its directors or officers,
the trustee has relied upon information furnished to it by the obligor.
 
Inasmuch as this Form T-1 is filed prior to the ascertainment by the trustee of
all facts on which to base responsive answers to Item 2, the answer to said Item
is based on incomplete information.
 
Item 2, may, however, be considered as correct unless amended by an amendment to
this Form T-1.
 
Pursuant to General Instruction B, the trustee has responded to Items 1, 2 and
16 of this form since to the best knowledge of the trustee as indicated in Item
13, the obligor is not in default under any indenture under which the applicant
is trustee.
 
                                        4
<PAGE>   5
 
                                   SIGNATURE
 
Pursuant to the requirements of the Trust Indenture Act of 1939, the trustee,
IBJ Schroder Bank & Trust Company, a corporation organized and existing under
the laws of the State of New York, has duly caused this statement of eligibility
& qualification to be signed on its behalf by the undersigned, thereunto duly
authorized, all in the City of New York, and State of New York, on the 3rd day
of December, 1998.
 
                                       IBJ SCHRODER BANK & TRUST COMPANY
 
                                       By:          /s/ LUIS PEREZ
                                          --------------------------------------
                                                        Luis Perez
                                                 Assistant Vice President
 
                                        5
<PAGE>   6
 
                                                                       EXHIBIT 6
 
                               CONSENT OF TRUSTEE
 
Pursuant to the requirements of Section 321(b) of the Trust Indenture Act of
1939, as amended, in connection with the issuance by Renters Choice, Inc., of
its 11% Senior Subordinated Notes 2008, we hereby consent that reports of
examinations by Federal, State, Territorial, or District authorities may be
furnished by such authorities to the Securities and Exchange Commission upon
request therefor.
 
                                       IBJ SCHRODER BANK & TRUST COMPANY
 
                                       By:          /s/ LUIS PEREZ
                                          --------------------------------------
                                                        Luis Perez
                                                 Assistant Vice President
 
Dated: December 3, 1998
 
                                        6
<PAGE>   7
 
                                   EXHIBIT 7
 
                        CONSOLIDATED REPORT OF CONDITION
                      OF IBJ SCHRODER BANK & TRUST COMPANY
                             OF NEW YORK, NEW YORK
                     AND FOREIGN AND DOMESTIC SUBSIDIARIES
 
                         REPORT AS OF SEPTEMBER 30,1998
 
<TABLE>
<CAPTION>
                                                                            DOLLAR AMOUNTS
                                                                             IN THOUSANDS
                                                                            --------------
<S>    <C>  <C>                                                <C>          <C>
ASSETS
1.     Cash and balance due from depository institutions:
       a.   Non-interest-bearing balances and currency and coin..........     $   42,702
       b.   Interest-bearing balances....................................     $   13,444
2.     Securities
       a.   Held-to-maturity securities..................................     $  191,921
       b.   Available-for-sale securities................................     $  118,931
3.     Federal funds sold and securities purchased under agreements to
       resell in domestic offices of the bank and of its Edge and
       Agreement subsidiaries and in IBFs:
       Federal Funds sold and Securities purchased under agreements to
       resell............................................................     $   79,838
4.     Loans and lease financing receivables:
       a.   Loans and leases, net of unearned income.........  $1,938,005
       b.   LESS: Allowance for loan and lease losses........  $   63,361
       c.   LESS: Allocated transfer risk reserve............  $      -0-
       d.   Loans and leases, net of unearned income, allowance, and
            reserve......................................................     $1,874,644
5.     Trading assets held in trading accounts...........................     $      462
6.     Premises and fixed assets (including capitalized leases)..........     $    1,922
7.     Other real estate owned...........................................     $      819
8.     Investments in unconsolidated subsidiaries and associated
       companies.........................................................     $      -0-
9.     Customers' liability to this bank on acceptances outstanding......     $      371
10.    Intangible assets.................................................     $   11,167
11.    Other assets......................................................     $   68,097
12.    TOTAL ASSETS......................................................     $2,404,318
</TABLE>
 
                                        7
<PAGE>   8
 
                        CONSOLIDATED REPORT OF CONDITION
                      OF IBJ SCHRODER BANK & TRUST COMPANY
                             OF NEW YORK, NEW YORK
                     AND FOREIGN AND DOMESTIC SUBSIDIARIES
 
                   REPORT AS OF SEPTEMBER 30,1998, CONTINUED
 
<TABLE>
<CAPTION>
                                                                            DOLLAR AMOUNTS
                                                                             IN THOUSANDS
                                                                            --------------
<S>    <C>  <C>                                                <C>          <C>
LIABILITIES
13.    Deposits:
       a.   In domestic offices..........................................     $  682,904
            (1) Noninterest-bearing..........................  $  135,253
            (2) Interest-bearing.............................  $  547,651
       b.   In foreign offices, Edge and Agreement subsidiaries, and
            IBFs.........................................................     $1,154,887
            (1) Noninterest-bearing..........................  $   17,024
            (2) Interest-bearing.............................  $1,137,863
14.    Federal funds purchased and securities sold under agreements to
       repurchase in domestic offices of the bank and of its Edge and
       Agreement subsidiaries, and in IBFs:
       Federal Funds purchased and Securities sold under agreements to
       repurchase........................................................     $   91,000
15.    a.   Demand notes issued to the U.S. Treasury.....................     $   12,693
       b.   Trading Liabilities..........................................     $      239
16.    Other borrowed money:
       a.   With a remaining maturity of one year or less................     $   31,002
       b.   With a remaining maturity of more than one year..............     $    1,375
       c.   With a remaining maturity of more than three years...........     $    1,550
17.    Not applicable
18.    Bank's liability on acceptances executed and outstanding..........     $      371
19.    Subordinated notes and debentures.................................     $  100,000
20.    Other liabilities.................................................     $   76,658
21.    TOTAL LIABILITIES.................................................     $2,152,679
22.    Limited-life preferred stock and related surplus..................     $      N/A
EQUITY CAPITAL
23.    Perpetual preferred stock and related surplus.....................     $      -0-
24.    Common stock......................................................     $   29,649
25.    Surplus (exclude all surplus related to preferred stock)..........     $  217,008
26.    a.   Undivided profits and capital reserves.......................     $    4,112
       b.   Net unrealized gains (losses) on available-for-sale
            securities...................................................     $      870
27.    Cumulative foreign currency translation adjustments...............     $      -0-
28.    TOTAL EQUITY CAPITAL..............................................     $  251,639
29.    TOTAL LIABILITIES AND EQUITY CAPITAL..............................     $2,404,318
</TABLE>
 
                                        8
