I tend to avoid recommending specific exercises - instead I like to recommend that you think of your trunk in three dimensions and apply weight bearing loads to at least every 90 degrees around that circle (which implies at least four exercises).

So that would mean your flexing your back, your abs, and each of your two sides (Abdominal external oblique, I think).

I personally try to hit every 45 degrees (which implies at least 8 exercises).

You need to try a lot of different exercises and find the ones that work for you and for your body type.

And you need to walk.

You can do 50 different trunk/core exercises and you will never hit every single muscle and combination of muscles the way that walking does.

Your body is a walking machine. You were built to walk. Walking will heal you. It will be painful and difficult at first - when I blew out my L4/L5 I needed to lie down for an hour after walking 4-5 miles. That doesn't last. Your body will tighten and strengthen up all the right muscles to hold your back in the most natural and healthful position it can be in - the one that supports walking.