I would say that any type of upper body workout you can get into will help. Obviously, bench press and tricep exercises will help build upper body strength for pushups. The key though, is endurance.
When you go through your initial training, you'll get 'dropped' for everything.....uniform not up to par, goofy expression on your face, being too "Hooah," getting sick, asking a stupid question, eating too slow, you name it. Depending on your training and the cadre, you can literally expect to do at least 1000 pushups a day.
In other words, having an upper body like Arnold Schwarzenegger isn't going to help you with military pushups. You want to develope strength, but also be able to pump them out all day long.
I'm no fitness guru, but I would suggest getting in the habit of doing pushups all the time....do a set when you get up in the morning, another before breakfast, before lunch, before dinner, and again before going to bed. Elevate your feet (on a chair or something...at least) and do four count pushups: "1, 2, 3, ONE; 1, 2, 3, TWO; 1, 2, 3, THREE..."
Do widearm, closearm, diamond, regular. ... ...
Do this in conjunction with your normal workout program (running, weights, etc). Hope this helps a little.
Good luck! Now, go beat your face!
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