What are the specs (specifically HD, RAM, and processor speed? There are a lot of decent processor upgrade for beige G3s, btw...
I would stick with 10.2 if it's running everything as you want it run. I'd go to 10.3 if your RAM can handle it, but it's WAY more of a RAM hog and takes up more HD space, depending on your install. Half our OSX machine run 10.2 and the other half run 10.3. The G3s run 10.2, but that's mostly because they are lower end...