Exercise is, in general, a good idea. However, if someone has chronic lower back pain, exercise should always be cleared with your doctor or physiotherapist first. Depending on the type of injury that is causing your pain, certain exercises could worsen the pain.
As for buying equipment, many exercises you can do to strengthen your body do not need expensive equipment. If you haven’t seen a physiotherapist, ask your doctor if you should. He or she could advise you on different techniques to help your back pain and prevent recurrences.