A:Normally Id suggest you start over. Bike design has progressed a long way since 1997. But the F500 (new, $1,000 or so) is a fairly well-regarded bike. Good frame, solid construction, a little on the stiff side but a capable cross-country bike.
So, probably worth upgrading. But I wouldnt go overboard. I think it would be entertaining to go mostly SRAM, just to break from the ordinary. A nice start point would be SRAM X.9 Twist Shifters ($85), designed for nine-speed. I think youll like grip-shifting. I find it intuitive and it works well. Add a SRAM X.7 rear derailleur ($65), SRAM X.7 front derailleur ($35), and SRAM PG-90 rear cassette ($70), and a SRAM crank XX Crank ($429). Nice setup. Tekro M530s are nice brake calipers ($90 a set). And, wheels...maybe Rhyno Lites on Shimano XT hubs, $275 or so.
The big question is: Are you going to do this yourself? Its not hard, and likely entertaining. But it also takes some tools and a little bike know-how. If you havent got a good tool set, Id suggest just going to your local bike shop, tell them what you want to do, and let them take over.