In a nutshell, yes, do a lot of shopping.
When you aren't just an employee with a W-2/paystub to show a lender for your income there are going to be a lot of variables to consider. Many will require a signed lease in order to consider any rental income at all.
I've never asked a lender for a written list of underwriting rules but most loan originators should be able to answer any related questions up front before you apply, especially if you can give them your FICO scores and a list of all minimum monthly payments.
Make SURE you get a good faith estimate and compare all of the expenses when deciding which lender/loan to go with.