For the one arm push up in particular, I would recommend following the advice in Al’s one arm push up tutorial, which can be found in the Tutorial Database thread at the top of the forum index. Pick a variation that is appropriate for your level.
Other than that I definitely recommend pistol squats and back bridges. For upper body pulling I would suggest pull ups, and you may also want to work on one arm Australian pull ups. If you want more core work, I would suggest either hanging leg raises or L sits.