I have used a method where you take our goal number (say 100 push ups) and then you do as many push ups as you can, let's say 30 just to pick a number, have a short rest, then do as many as you can, let's say 20, then repeat till you get to 100.
So a days push up training day one might go:
30, 20, 15, 15, 10, 5, 2, 1, 1, 1 =100
Next time it might be:
35, 25, 20, 10, 10 =100
Etc etc till you can do 100.
Same applies to dips, chins, crunches etc etc.
Re the beep test a personal trainer mate of mine trained for the TOU (Tactical Operations Unit in the NSW Police Force) one of the toughest entry requirements in Australia, these guys are freaks, unfortunatly he did not pass the week long assessment, he did however pass the entry physical test that he trained for.
He said to vary where to start the beep test, don't always start at zero, start it at 6 or 7 or what ever so you can push the upper end and get used to what 10 and 11 and 12 etc feels like, then after a bit of training in the upper levels do the whole thing to test yourself, then repeat the whole cycle again.
Good luck with it all.