Find a workout partner. If you can't, compete against a clock (including pushups).
Get your recruiter to teach you correct pushups. LEarn the technique. Do as many as you can in a minute. Rest or switch to crunches. Try to beat the time.
Favor doing correct pushups over quantity. At this stage, you have no one to impress with numbers. Learning the technique will save you time and hollaring.
Regarding running, build up endurance. Find a high school track. Run a quarter mile at a time. In between, don't stop. Just do a slow jog or, preferably (in my opinion, a fast march. Keep it going until you run at least two miles.
Not as important to stretch prior as it is to stretch following.
I also advise against running with any weight on your back until the Corps has strengthened your back enough.
To recap, use the clock or a workout partner to push you. Quality of workout is more important than quantity. Stretch following the workout. You can eat, but there's really no need. Your workout won't last as long as you think and the food in your stomach won't get digested in time to give any energy boost. So, exercise in the morning before you think you're hungry. Commit to the workout as if it's a part of the normal routine. Just like you shower everyday (presuming), you workout everyday.