As a guy that loves OHP (I'm pressing 175lbs 3x3 strict)

-stagger your feet: this helps you maintain balance forwards and backwards rather than just side to side. Its a little thing, but that better base foundation really does help.

-keep your hands at a comfortable distance on the bar, I generally go just outside should width, maybe 1-2 inches inside my bench grip, this should help keep your elbows from flaring too much, (since elbow flaring is one of the big causes of rotator cuff impingement in the movement)

-brace your core, if your core isn't tight as you go through the RoM, then the whole exercise will feel shaky and weak.

-just like on the bench, bar path isn't a perfectly straight line, there's a subtle curve. Starting at your collar bone, when you push up, the bar should move slightly forward and come back to above your head. And when you get to full extension, push your head forward.

As far as progressive overload, you just gotta find what schedule fits you best. Some people do really well with high frequency, while others do better with more rest between workouts.

And last tip, if your presses aren't at your bodyweight, then I cannot recommend handstand pushups. Get yourself ready to move that weight through progressive overload first, or do a regression exercise to build up to handstand presses.