There are a lot of factors that will determine what you are eligible to be approved for. This is a list of a few
Credit Score- FHA & VA loans are more flexible and may have options that will go below the standard 620 credit score. To qualify for the minimum down payment for FHA, the FHA requires a score of 580. Ideally for the best interest rates and terms 620 and higher is optimal. For conventional loans Fannie Mae and Freddie Mac both require a 620 credit score, unless you are eligible to refinance under the HARP program.
Income- In most cases your income needs to be documented to determine that you have sufficient income to make payments on your mortgage. The amount of documentation may vary depending on type of income and loan program.
Down Payment- The source of your down payment needs to be documented. If the money is already in your account an account statement would be needed. If there are large deposits showing on the current statements the source of those deposits will need to be explained. The main ineligible source of a down payment is the seller of the property(unless it is family), the realtor or the mortgage company(sorry), but a gift from family or a close friend is acceptable.
This is a quick checklist of standard documents which may help expedite the process
Copy of Driver License OR Government Photo ID
2 Most Recent Paystubs
2 Years W2's or Tax Returns
2 Most Recent Bank Statements or/and Asset Statements