As you mentioned, going for a certain amount of reps, and then when you reach your goal moving up, is another good routine. That way you know you are getting stronger because you can do the same amount of reps you used to, but now with more weight.
I pushed myself to exhaustion today.
I did 50 pushups thinking that it was gonna be a day off for me and wanting to do at least a bit. I did the 50, then I did another set of 40, then a set of 30 in 30 minutes. I also did a lot more repetitions of everything than usual. I'm feeling pretty good. Exhausted, but good.
Be sure to drink plenty of water! It will keep you hydrated and ready for more.
Also, rest is also important. If your muscles are very tired, there is nothing wrong with doing some excersies to work out the soreness, but if you work out really hard for days without getting rest, you can actually damage muscle tissue. If you try to do pushups tomorrow and you find you can only do a few before it starts hurting real bad, stop, do some arm stretches, and take a break.
Also, last year I loved my coaches, and I'll be the last to criticize anything any of my coaches do but the dude playing safety next to me had no idea how to play football, he missed tackles everywhere, couldn't catch and wasn't fast at all but he got so cocky from getting to start. One of the dumbest kids I've ever talked to too.
This year, I have no relationship at all with the coaches, my first year, my head coach was also my history teacher and a general nice guy and my assistant was a nice guy as well. The senior coaches are more strict and stuff and I have no relationship whatsoever with them, so I'll have to adjust.
It is important when doing strength training to actually give your body some rest. If you do a workout focusing mainly on the upper body, the next day it would be better to work the legs to let your muscles recover. Actually working the same muscles every day could stifle the improvement in muscle strength. Our fitness coach got some training manuals from NfL sides and it was noticeable that they would work upper body on Monday/Wednesday/Friday and lower body on Tuesday/Thursday/Saturday..