I have back issues as well. Just had a partial Laminectomy and Bi-Lateral Rhizotomy done at L5-L4 about 6 weeks ago.
I've found that planks and hanging leg raises are the best core exercises for me. The hanging leg raises (hanging from a chin-up bar) are great because they strengthen the abs while also strengthening the lower back at the same time. You just have to make sure you're not "swinging" the movement.