Just to throw this out there, i never do pushups, yet i can still max it out easy. Any powerlifting or bodybuilding routine you will get enough muscular endurance to do 70-some pushups. Obviously doing situps enough, you will be able to pretty easily be able to do the Army standard of around 80 as well.
The only thing that won't come naturally if you're working out, is the running. I don't like doing cardio as i am a bonafide ecto, so normally i run about a 14 minute 2 mile. A little bit of work and i could get 13 minute 2 mile pretty easily.
I guess it depends on your goals. If you just want to stand out on the PT test, train for the PT test with body weight exercises.