Don't take any of this as sound medical advice because I don't know what your back problems are, but I had back surgery almost three years ago and have been to WDW about 7 times since then. I go on everything despite what the warnings said, I asked my doctor if I was okay to ride anything, he gave me the go - so I went all out.
Some rides that bothered me before I had my surgery, and still do now are Dinosaur (If you do ride it, request a seat in the middle of the back row because it won't jerk you as much), Primeval Whirl (when it spins, it can slam you into the side if you don't have a full car). If you're going to the water parks, I would avoid any slides (like summit plummet) that don't have a raft with them because most of the time your back ends up right on the slide and it can make things worse. Space Mountain can make me a little sore sometimes but no where near enough to make me not want to ride it.
I hope this answers some of your questions, let me know if you have any specific questions about rides that i've been on and been fine or had problems with!