Credit
There is no federal minimum credit score on a conventional loan, because nothing federal insures it. Fannie Mae sets no minimum score for a file run through its Desktop Underwriter, and at least 620, with exceptions, for one underwritten by hand, and lenders are free to require more than either.
The automated underwriting
A conventional file is run through Fannie Mae's Desktop Underwriter or Freddie Mac's Loan Product Advisor, and the engine returns what the file needs: how much income documentation, what reserves, what has to be explained. That answer is a far better guide to whether you qualify than any rule of thumb.
The rules each lender adds
A lender is free to require more than Fannie Mae or Freddie Mac does, and those extra rules can differ from one lender to the next. One lender's no is not always conventional's no.
Income and debts
The payment has to fit your income alongside what you already owe, and the income has to be documented in a form the engine and the underwriter will both accept. Self-employed and commissioned income can qualify; it takes more paper, not a different program.
The property
A primary residence or an investment property of one to four units works, and so does a one-unit second home. Condominium projects are where conventional guidelines get specific, and a project a lender will not finance is much better found early than late.