I'm not Cathe but.......I could give one recommendation for those working out at home. In my experience pull ups are THE BEST exercise for the back. They're great for so many reasons--they target the entire back, you can do them at home, you use your own body weight for the exercise, you can change hand positions to target different areas of your back, you can use an assist w/another person who just has to give you a little push from below.
There are a wide variety of pull up bars available from places like Sports Authority, Bigfitness.com, etc. etc. You can get a pressure bar or you can get one w/brackets so you can remove it when you're finished working out.
You can start out slow--when I first started doing pull ups my goal was always 30 but I began by doing like 6 sets of 5, then 5 sets of 6, etc. etc. until I worked my way up to 3 sets of ten.
JMHO--pull ups are one of the most effective back exercises.