reaching exercise goals

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Eventually I want to run 1.5 miles in 13:30, do 39 pushups (in <2 minutes), and 87 situps (in <2 minutes). I have these goals because I'm in the Navy and I want to do well on my physical assessment test.
I started trying to lose weight as a way of trying to improve my run time, as well as finally working through couch to 5k. Endurance is much improved, but speed isn't there yet (16+ minutes on the run). I can do 18 push-ups, and 60 sit-ups.
I can train, and I have been working on it, but I also want to make sure my diet supports these goals. Is there any way to manage that?
I don't really care about weight loss; I'm happy to stay at my current weight. I just really want to do well, and improve my scores over time.