Your problem is so familiar for me. This January I started a running program: training for a half-Marathon. My lower back killed me during the first month both meanwhile running or sitting. Then I started a core strengthening program: Pilates, exercise ball, back maintenance 5x / week. My "bible" was a wonderful book: The Healthy Back Exercise Book by Mr. and Mrs. Fielding.
In a month my backpain disappeared, and did not come back even when my long run reached the two hours.

As a start good running shoes are the basic. Try to find smaller, more personal stores, where usually there are some more experienced helpers.
The owner of the small store where I bought my shoes spent 40 minutes to watch me to run in dozen different shoes before giving me the perfect ones.

Good luck for your running - for me it was the real miracle, that helped to fight back my slowing metabolism.

Hope to see you next fall on the Marine Marathon in DC.:-)))