Best workouts for a bad back(lower).

Years ago I broke my L5 vertebra. So I deal with back pain a lot. I went to PT last year and they gave me some stretches to do to help my back. Apparently my hips aren't centered either. Now that I'm 33 my stomach is starting to grow a lot. I'm 6'6 and have weighed about 185 my whole life. Now I'm up to 205. It all goes to my stomach and butt. So my question is what are the best workouts to do for someone with a bad lower back that will strengthen my core and also help flatten my stomach. I started doing some workouts on here that focus on lower body and core. I just want to be sure I'm doing the right things. Thanks!