So guys, I've been going to the gym for boxing/muay thai for the past 2.5 months, and although I feel I've lost a bit of fat and have a bit more muscle, I still feel really weak. So I've been thinking of adding a workout routine to my schedule that can get me stronger. In particular, my arms and legs. Whenever we do squats/walking squats, I always feel like I'm pushing myself to the limit, yet still have to stop every now and then to rest. And for push-ups, we do the kind where after the push-up we angle off to the side and hold on arm up (kid of like in a fallen T position). When we do this, my arm seriously starts to shake and I'm afraid if I push myself too hard it'll snap.
Right now, I'm thinking simply doing squats and push-ups at home is a good start. Is that a good idea? If so, should I stick to a routine (like 10x10reps) or try to gradually increase the number I'm doing over time (like, should I try to push myself to do as many as I can)?
Not sure if it matters, but I'm male, 5'10", 25y/o, and 156 lb.