Do your upper body workout AFTER your pull-ups. Your muscles will be exhausted by the end of your workout and you won't be able to do many pull-ups. Your training should be sport-specific. Since the Marine Corps is big on pull-ups, you want to prioritize those. Push ups the morning after: yes, in moderation. 2 or 3 sets of your max won't affect muscle recovery; any more will. One word: PROTEIN. Lots and lots of protein.