Whatever you do, don’t get a cheap exercise bicycle. I bought a $100 or so one from Sears maybe 20 years ago and was [b]very[/b] aggravated by the irregular pedaling motion. I finally just hauled it to the dump!!
If you’ve got a bad back, I’d also suggest you avoid the NordicTrack skier. That was my next machine and, while it is low impact, it requires a good sense of balance – which, for me at least, put a lot of pressure on my back.
I now use a True treadmill, which is excellent. The running platform is mounted on rubber spacers, which reduces the shock to your knees and feet. Despite having arthritis in one of my knees, this does not give me any problems.
However, it does take up quite a bit of space and forget about taking it up a flight of stairs!! It’s also pretty expensive.
Good luck!!