I'm not a doctor, but I have played one on the internet.
First, get the ok from your REAL doctor.
I've pulled lower back muscles, as well as slipping a disk, after that experience I don't know that cycling would be a good "recovery" sport. On road bikes the body leans too far forward to be alleviating, MTB is just hard on the body all the way around, and in fact I wrenched my back this weekend trying to muscle up a hill. If anything, the recumbent might be the best choice, but I don't know much about them.
Finally, as norco suggests, one of the upright comfort bikes coupled with relaxed pacing around the neighborhood might work out ok. Good luck!
oops, guess that didn't really answer any of your questions. Sorry.