some okay advice in there. As they mentioned, you will be sore. If you are too sore to run, walk. Too sore to walk, rest a day but then get back out there.
It sounds like you are really out of shape and have limited time. The most important thing for you is to do the exercises you will be doing at boot (jump squats are no help ir push ups or running). Talk to your recruiter and he will probably have a workout for you. Many times they will even arrange to have a group get together several times per week to prepare new recruits for boot.
Last, for your push ups, there is a concept out there called greasing the groove. If you suck at push ups and can only do 15, then every time you enter your bedroom, walk out side or some other easy marker, drop and knock out ten. try to get 100 in a day. When you do that, start doing 11 or 12 whenever you pass your mark. depending on the time you have left, you should be able to work up to at least a couple hundred per day.
The one exercise I encountered in boot that surprised me was the front leaning rest. Just stay in the push up position, locked out, for a couple minutes. You'll understand what I am talking about after about 30 seconds.
Oh, and you may want to work some leg lifts. Often drill sargeants use butterflies, supine bicycle and leg lifts to smoke recruits. Best of luck, I reallyenjoyed my Basic Training experience.