You'll fill out the federal and state firearm transfer forms and go through a criminal background check performed by the state police. There's absolutely no reason to check your credit since finances have nothing to do with the legality of firearm ownership/transfer.

I see that not all statesare permitted to allow dealers to contactthe state authorities forthe NICS--some FFL dealers contact the FBI directly.

http://www.fbi.gov/hq/cjisd/nics.htm