Upper Body Strength and Toning?

Santa14

Hi I just recently began this journey, in attempts to become a sort of "example". I currently attend High School, and right now its summer time so why not start getting fit? Well, I am the Battalion Commander for my JROTC unit, and I was told I have to be in a good shape to set the example. Now I can endure running as my family has a long line of track runners my last mile test being 7:13, but I wanna know if it is an effective way of burning fat? I do situps, and pushups at a rate of 30 push ups and then I blow, and 56 Situps and boom blow. I can't really even take weights when it comes to school or any athletics during the year except for our PT team (once a week) as I am up to my butt with AP and IB work that takes up alot of my time. Are there any good tips on quick routines i could do in the morning before I leave? Also I was thinking about buying this "MAX Out the Army, Navy, Marine, and Air Force Physical Fitness and Combat Fitness Tests" http://www.amazon.com/Marine-Force-Physical-Fitness-Combat/dp/0978575334 as I heard good things about it. My ultimate goal is to just burn the fat, enough to the point where I can lose it. I don't really want to gain muscle as I have no time like I said during the school year to really work out alot, but I want to gain strength to be able to do more than a pull up haha, I know pitiful.