Gargy!!!!
You're off to get fit and you didn't email me? I'm hurt
There are so many different ways to lift that actually decompress the spine.
For instance, most people do bicep curls standing (pretty tough on the back) or on a curl bench (better). But try taking a bench over to a high pulley machine. Connect a flat, short bar to the high cable pulley. Lay on the bench on your back and pull the bar to you, bicep curl style. Not only does it decompress the back, but you can't cheat.
Doing chest flies on a decline (kinda upside down) can also decompress your back.
I also gotta agree with GHoosdum. Gradually build your core. Since it's a sensitive area, you'll have to see what works. I personally like medicine ball work and giant inflatable ball work.
For lower back pain I also swear by spinal decompression therapy administered by a chiropractor and a dang good mattress.
YOU GO MAN!