Not all back pain is the same. I happen to be a bit sway-backed - my lower back bends forward a bit more than is normal. When I started commuting on a hybrid "comfort" bike with a very upright Mary Poppins sitting position it nearly killed my back. Then I started riding my old touring bike with drop handlebars and the pain went away instantly. For others whose back is sensitive in the other direction drop handlebars are torture and upright is the way to go. I've found a middle ground is best in the long run for me, not fully forward but not back on my seat either. But my back overall has gotten so much stronger from riding it isn't much of an issue anymore.

I was just over the posted 200-lb Clydesdale level before starting to ride and do yoga stretches. Almost 30 pounds lighter now, normal for my height, and holding steady eating pretty much what I want (within bounds of reason). Concentrate on having fun and being comfortable rather than logging miles and "training." Find a bike that not only feels right but looks cool and gets you psyched to be on it. Easy and frequent is better than hard and seldom. Even a leisurely ride burns tons of calories. If you like to bike, you'll bike a lot, and the rest will take care of itself.

Consider a steel touring bike. They're solid and fun to ride and built to carry weight comfortably over long distances. The Surly Long Haul Trucker or something like it would rock I think. But you could probably find an older touring bike in decent condition for not much money that would do about as well.