It's a great book but it is very confusing for most people.
I did a thing where I would do 2 pullups every minute for as many minutes as i could - went from 5 minutes to 9 in one month and in that same month I went from being able to do 3-4 in a row to being able to do 7 in one shot.
As far as running, run everyday - in a year you should go from 22 to 19ish by just running everyday.
Learn how to set up a week of training and you can go 18ish in a year.
Long run once a week, 2 threshold runs a week, and the rest easish and maybe a 2nd medium distance run (almost a long run, but not quite).
For situps just do them every day.
No offense to the marines but there standards are not that hard to attain. Just by being a person who works out everyday for a year maybe two gets you to the standards or well below them.
Don't be afraid to gain some weight also, the 3 mile race, as crazy as it might sound to a 22 minute runner, is very similar to the mile, which has a huge anaerobic power component to it.
Btw i'm the same height as you and ran a 17:45 5k (3.1miles) at a similar weight. and the year befor i ran a 22:55 best. I trained like a newbie because I was one all year long - and still came out decent.