I definitely don't have as bad a back as the OP, but as someone who recently purchased a used bike that needed some break work and the like, I can attest that a mountain hybrid with a good seat does wonders for you. I had a mountain bike before this (must cheaper) and it hurt my back. Yesterday, I rode 10 miles to get the thing home over some pretty steep hills and am not hurting at all in my back, as I was used to as a teen riding around on my old bike. No suspension, nothing fancy. The frame fits me really, really well, which I think was the difference.

Go look and find a bike that fits. I went to an LBS and was fitted for a frame the day before I got the bike. They were super helpful and didn't pressure me to buy the bike there. I bought enough accessories otherwise to work on the bike I did buy! Altogether it cost me $200.00 with a basket for commuting and I am truly happy I did it. Spend money and find a bike that will properly fit you and then add in a better seat perhaps better tires, etc.