Jack, a handy tool to have at this stage, is one of those "Impact" screwdrivers. The ones that when you smack them with a hammer, they rotate. Great for stubborn hinge screws, brake drum screws, etc. K&D makes a good one, and they should be available at any good parts store. Remember too, that most of the screws are PoziDrive, not Phillips head. McMaster-Carr sells PoziDrive bits in all the common sizes.
Jeff