Mongo is right about the fire barrier. It will cost a lot more to put up a comercial product than drywall. Installing a drywall ceiling is not much differnt than doing a wall. Once again purchase a good Home improvement book. The hardest part is getting the sheets into the basement. Rent a tilting drywall jack, this will make quick work of lifting the sheets to the ceiling joists or you can do it the old heave-ho method and use a "T" brace to hold the sheets against the joists. Use 1/2"ceiling board or 5/8" fireX if the joist are on 24" centers, you can use regular 1/2" drywall if the joists are 16" O.C. While you are at the rental yard also rent a screw gun to screw the sheets up, use 1 1/4" drywall screws for 1/2" rock and 1 5/8" for 5/8" rock While your at it install unfaced fiberglass insulation before you drywall.