When I was in the Army I used the pyramid routine (mentioned above) to increase the amount of push-ups I could do during a PT test. I would go to 10, then work my way down. Which I believe comes out to 110 push-ups. I couldn't finish it when I started out.... I think I got through 80 push-ups or so. I was doing maybe 65 in two minutes at the time during my PT test. I eventually got to where I was doing the Pyramid routine up to 12 while propping my feet up on my bunk. After that I was doing 115 in two minutes during my test.
Just remember that if your goal is to increase the amount of push-ups you can do, then that's an endurance work-out! Weight training might assist you in training the muscles needed... but unless you're lifting with endurance (high reps) in mind it won't do much good. I've seen pretty big guys that can't do 50 push-ups. I'm pretty lanky, I can do well over a hundred without stopping. something I currently do when I don't have access to a gym is I wrap a "JumpStretch" band across my back and hold it to the floor with my hands while doing push-ups. The bands are awesome, and you can use them later in weight training routines also.
As far as running, Take short slow jogs. Don't worry about distance. Once you feel like you won't blow your knees/lungs out, try an interval method: jog two minutes, sprint 30 seconds for your run. As your endurance improves you can increase the amount of time for your total run. You can also decrease your jogging time, and increase your sprinting time. For example, if you're running on a track, jog a lap, sprint a lap. This method of running kept my two mile times under 13 minutes my entire time in the Army. It's not track star speed by any means, but it's fast in the Army! good luck dude.