In your situation the standard recommendation is to go with one of two guns. Remington 1100 or Beretta 390/391. Both are soft shooting guns and are reliable.
Back pain is no fun when you shoot.
Some tips for people with sensitive backs.
Learn to swing your body and gun from the legs rather than from the waist. Takes pressure off the back and the swing is more level.
Make sure the butt of the gun is in the shoulder pocket and learn proper shotgunning stance. Don't stand up straight like you would with a rifle, lean slightly into the gun (slightly, don't fall on your face trying this!).
Think about getting one of those golf cart takeoffs for shotguns so you don't have to carry a heavy ammo bag. Some guys make them from golf bag carriers they rescued from the trash. This is especially important in games like Sporting Clays but is usefull for Skeet and Trap too (Placed behind the firing line of course)
Pop a couple of your favorite pain killers before you shoot. Non prescription products of course
My favorite is Aleve, helps when my back is acting up.
If you are really in pain, stay home! Shotgunning will make it worse! I know, I speak from experience here, more than once
If it hurts to do it, don't do it. High driven birds in Sporting Clays are death to bad backs
Take up Sporting Clays, you might run into a good chiropractor.