Wouldn't it be best to get a good faith estimate that includes estimated closing costs?
a) gather general info on rates and fees offered.
b) choose the approximate one for you.
c) apply, nail it down.
Closing costs vary, but aren't they similar one bank to another? A small difference shouldn't be the deciding factor.
a) I looked on line and asked a few brokers. LAX_Esq wants to call many banks, then try to get each bank to give the same rate as the cheapest.
b) I chose based on what would give me the lowest total cost. I paid points because the numbers worked for me.
c) If you're still deciding between more than one, get a 'good faith estimate' or whatever.
Note: Don't give out your SS# in the exploratory stages. They should have published rates. But if you do have several mortgage pulls on your credit report, it's OK - they won't count against you - if they're all within a certain time frame. (6 months?)