I use a trackball for my computer and am an avid gamer. I play many different games (a lot of minecraft, lots of FPS games, lots of RTS games, etc) and feel that I am just as good with the trackball as I used to be with a mouse. I'm also a software engineer, so I use my computer a very large amount of time every day.
Making the switch to a trackball is definitely something you can do and still successfully game. Not everyone likes trackballs, though, so you may regret your purchase. One thing I would stress is that you should try to force yourself to adjust to the trackball if you want to learn to use it. Unplug your mouse and put it away. Make it so your only option is to learn how to use your trackball or don't use your computer. You WILL have to spend some time adjusting, and during that time you WON'T be as good at games as you had been. Don't fret - just keep trying. I'd say I was back to the same skill level within about 2 weeks, but it may be longer or shorter, depending on how well you adjust.
As far as recommendations, I've only ever used one model, the Logitech Trackman Wheel. You may have better luck going into a B&M store and trying out different models and find one that suits your hand shape.
Either way, I'd highly recommend attempting to switch if you're considering it. I haven't regretted my decision in the slightest.