I've basically been told I'm free to do whatever my body allows me to do. My break happened over a year ago and the only thing I'm not allowed to do is bend backwards. I'm also supposed to avoid heavy lifting, running, jogging to much. If I go at a reasonable pace I can ride an elliptical, bike, or stair machine. I just get bored and would like something new to try.
I think you're going to get a lot of suggestions, but none will necessarily apply to you as we're not you. Have you asked your orthopedist for suggestions? Or seen someone who specializes in this, such as a physical therapist? I'd think after a trauma you would want to get back to exercise slowly and build your muscles that support your back before plunging back into it. There are also therapeutic yoga practices that tailor the exercises to what you're able to do and that specifically apply to what you're dealing with. It would be more expensive and probably entail one on one sessions, but it might be something to look into if yoga is what you like to do.