Last 2 or 3 is enough. Discuss this with your new H-1B attorney.
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USCIS usually requests the copy of the 3 most recent pay stubs. For more details discuss with employer's immigration attorney.
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There is no minimum number of pay stubs, esp. since you recently commenced employment with this employer. The situation would be different if you were employed for a lengthy period of time, when 2 or 3 months of recent pay stubs plus W2's would be helpful.
In your situation, the H1B transfer petition requesting extension of status can be filed now by another employer, but you may still want to consider a consultation with an immigration attorney in case there are other issues that need deliberation.
Pay stubs are evidence for maintaining status. If you continue to maintain status, you should not worry about the number of pay stubs you have.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. You are encouraged to seek independent and private counseling for a complete review of your case.
The typical approach is to submit the two most recent paystubs from the current H-1B employer with an H-1B change of employer petition. USCIS generally expects to see two recent paystubs and may request such evidence if not provided initially with the employer's Form I-129 petition.
** This response is for general informational purposes only, is not case specific, and is not for the purpose of providing legal advice. You should consult your attorney to obtain advice about any particular issue or problem.