There are 6 important exercises, in my opinion: squat, deadlift, bench, overhead press, chin/pullup, and row. Everything else is optional. Focus on the basics, get that down, then decide what else you need to supplement, if anything. You can sub in other exercises for squats and deads and still get results, but I would not do this if it wasn't absolutely medically necessary. If your physical limit is a body-weight squat, there is nothing wrong with that. If you can add some weight little by little, that's even better.
As far as sets and reps, if I understand your post, you are going to failure on even the warm-up sets. Let me know if I am mistaken. If that is what you are doing, I would change strategies. You want to have only one set per exercise near--but not to--failure, and that is your top or your last set (maybe also a "finisher"--a lighter weight, high rep set after your top set). For example, let's say you want to work in the 10 rep range. if you are benching, and your 12 rep max is 135, you could warm up with 45 x10, 65 x5, 95 x5, then hit 135 for 10, then rep out with a 95 lbs. finisher. Next time you bench, you want to either add a rep or 5 lbs. to your top set. over time, this really adds up and its how you get stronger.
If you want to go 3x10 or 5x5 with the same weight as a top set (some people prefer this way), warm up in the same fashion, but make sure you are using a weight for your work sets that you only get near--but not to--failure on your last set. If you are on your last set of a 5x5, and you get to 4 and you might not make 5 reps, stop at 4. Next time, get the 5 reps. Again, you want to add either a rep or some weight the next time you lift.
There are lots of different ways to do it, but going to failure on lighter weights before you get to your top set is unnecessary and counterproductive. Use the warm up sets to get you primed to work with the heavier weight, not to exhaust your muscles before you get there. This key is to keep progressively adding weight slowly over time. At some point, you will want to start wave-loading the sets and reps, but that is not necessary when you are just starting out.