As far as the bad back, two surgeries and a nasty infection left me without a disc at L4-L5 (the very bottom one) and I have some words to say regarding lower back issues:

Get a bike which has you riding with at least a somewhat aggressive posture. At first it seems like bolt upright would be good for someone with lower back pain, but it isn't. Upright will compress your entire back, and put loads of pressure on the problem area. An aggressive posture will stretch out your whole spine and make it into a sort of suspension system which will eat up most of the shocks in the road.

I can still ride upright, but not for incredibly long distances... and if your problem is also your lower back, I would definitely recommend you get a properly fitting road bike. Not necessarily racing, but handlebars 6 inches above the saddle is WAY too high.