Bodyweight squats really don't have enough load on the hip extensors to work them adequately. Even the barbell squat mostly targets the quadriceps (full depth Olympic/front squats involves the glutes a lot, and squatting low bar powerlifting-style involves the hamstrings).

Incline pushups (ie with your feet on a box) will involve more deltoids and less pectoralis. By continually increasing the incline, you can progress the difficulty of the exercise until you're doing handstand pushups.

The recommendation I make for folks is to buy an adjustable dumbbell set. Small cash investment, minimal space investment, and adds a bunch of exercises you can do. I've expanded the set with a pair of 10s and a quad of 25s, so the max weight I can put on a handle is 125lbs, and it holds up great.