Upper body, definitely push ups! Bicep curls, 2 and 3 point dumb bell rows, shoulder presses. T-push ups. If you can, get one of those pullup bars that hangs in a door way, pull ups are great!
Lower body. There are lots of variations of squats, lunges and step ups and dead lifts.
2 other items I would have at home, a stability ball. Great for dynamic stability and ab work. And a set of suspended rings like gymnast compete on. You could hang them from the pull up bar. They are great for all kinds of body weight moves and stability and balance.
Check out Youtube for lifting/strength.stability ball and ring training vids.