As a purist, I’d say watch them all and in release order, but if you really have to be choosy with your time, here’s a list of things you can skip (in my opinion):
Star Trek Into Darkness
Discovery (whole show)
Picard S1 and S2
Short Treks
I know suggesting skipping Discovery outright is going to be seen as… extreme, but I suggest doing so only if time is a crucial factor. It’s a dizzyingly uneven show with the lowest points of quality in all of Trek. However, it also has some incredible highs and some truly great characters, so if you find the time to watch it, you should. And I know I’m in the minority on this, but I found Short Treks to be unwatchable.
On the flip side, Lower Decks is incredible, and Strange New Worlds is good. The third season of Picard is excellent. Prodigy is a little weird but it’s got a lot of strength. Star Trek Beyond is also a surprisingly good movie.