I tried figuring it out with no guidance as a carefree 18 year old and managed to have a very unclean handstand.
I tried relearning it properly as a 30year old and found out that a decade or computer work left me without the proper shoulder mobility to protract overhead with decent internal rotation.
As a result I can get severe neckpain (usually 4-6 weeks to recover) coming from overactive upper traps
I've slowly gotten to the point where I'm fairly well-rounded as far as being able to use core, pecs, glutes, lats etc. during various exercises, without overly taxing upper traps.
If I were to do things over again I'd probably start with a regular yoga practice just to get better mind-body connection and get full body strength to a decent baseline.
For handstands specifically you might check out this guy's video which imo is well thought out, thorough, designed for people not already in shape: https://www.youtube.com/watch?v=1XJ2zR5tE0I
From the same guy, I've been following a full body mobility routine which you may find useful too—seems to hit a lot of spots that get problematic through desk work: https://www.youtube.com/watch?v=E2SOrScNbww
Ive always tried to limit the amount of weight I do with these and do it at most every other day, vs say everyday !
Is definitely (weirdly so) one the exercises that always made me "feel good and strong". Its generally considered a "slow lift" and it can become quite meditative !