Most Crossfit Affiliates offer a free workout. It's a great opportunity to ask any questions you may have. The workout will also allow you to get a observe the coaches' styles and personalities.

Sure, injuries happen. I honestly don't think they are as serious or as rampant as some may claim. Injuries are bound to happen in any form of exercise. But don't take my word for it, Call your local box and give it a shot:
http://www.crossfit.com/cf-affiliates/ Find your state on the left

If you don't like, at least you have experience to base it on.
Good luck.