A few people on the forums have done Crossfit. I did it for a year in a Crossfit gym and it was an experience but in the end I decided that I am not a fan of the Crossfit method. Maybe it was my shoulder injury
. Shoulder injuries are one of the most common things with Crossfit and it happened quite a bit on the CF forums and our gym. I'm guessing at home it would be safer than in a gym. Just use good form and if you are using a timer, still take your time with the moves. Also start with a lighter weight than prescribed.
As for Paleo, I never did it and although people in my gym liked the concept of Paleo, they really didn't follow it as they found it too difficult. The gym would have 12 week Paleo challenges and some people could mostly stick to it for 12 weeks but they didn't beyond that. You can look into Paleo if you like but most people I've known who have done Crossfit didn't do Paleo.