I have an exercise ball from Dick's Sporting goods and the real trick to buying one is to get one for your height. The sizes and heights are listed on the box. They are portable, cheap, fun and effective. I worked with a trainer and learned a lot of exercises to do with the ball before I bought one, then it came with a DVD and I learned a ton more, you can work nearly every muscle in your body with this thing. Probably the best investment I ever made in a piece of exercise equipment!
As for falling off, yeah, it's pretty common, but I didn't fall as much as I though I would. I recommend trying it at home a few times before jumping on at the gym, just to get the hang of it and get over any fear that you have. The beauty of the ball is that it lets you work specific muscles with different moves but it is ALWAYS strengthening the core body muscles while you work. I use it as a chair while I am working at my desk and it works my abs and core, while boosting my balance at the same time.
to quote Tony the Tiger, "It's Grrrreat!".
Good luck,
Laura the Loser (and proud of it):cool2: