paulflexes saidI also picked up an inversion table - partially for the decompression, and partly for the inverted ab and oblique crunches. It's a fucking miracle machine for that.
Ditto - I have a degenerative disc and love my Teeters inversion table, best invention ever and something you could probably begin using right away for simple inversion (ixney on the inverted crunches until you're medically cleared). But it's hard to offer advice without more specific information as to your condition, and this doctor that says don't exercise - is he an orthopedist? Shouldn't he recommend you start exercise with a physical therapist? I'd get a second opinion.
I'm assuming that you should begin with a battery of stretching and physical therapy exercises for pain management because jumping into a more traditional workout regime might exacerbate existing imbalances. If you're prone to being thrown out of alignment I recommend that you avoid or at least be cautious performing any twisting torquing movements like oblique crunches. My gym has a lot of ab machines but my favorite is the Ab Coaster, which like inverted crunches works the lower abs but doesn't put any stress on your back - like the inversion table, it's only a few hundred dollars and if you only had room for two pieces of equipment in your home I'd get these.
Using proper form is more important than weights or reps. With a bad back I'd adopt a low weight high rep regime. Once you strengthen your lower back you can experiment with upping the poundages because one of the most demotivating things you can do is suffer a setback by injuring yourself. Keep in mind that you have to work your back and abs equally to better protect your back and develop your core. I'd use hyperextension (low back) machines before progressing to actual hyperextensions and light deadlifts and avoid high impact movements and P90X style workouts. For cardio, swimming's the safest bet.