I've had back and neck problems too, plus I have arthritis in my lower back, but fortunately one women I ride with is a physical therapist (PT) and another one is a chiropractor (sp?).
Both suggested getting a foam cylinder (approx. 4' long x 6" dia.) to put under my back and roll around on (vertically and horizontally relative to my spine) with on the floor. Worked great for me!
Plus I went to the chiropractor and she "adjusted" (that's what they call it) my back and neck (3 sessions), and now I'm riding pain free (neck and back wise), have a greater range of movement with my neck and probably as a result, am riding stronger overall.
So, as others have suggested, before you go making a lot of expensive bike purchases, make sure your body is as good as you can get it (within reason, of course). I'm 60 years old as a point of reference.
Rick / OCRR