A quick rundown of what is out there:
TOS - the original series - I don't think it holds up too well, only watch if you get into Trek.
Suggested episodes - trouble with tribbles and balance of terror
TNG - the next generation - the basis of modern Trek. Probably what most people think of with star Trek
Eps - measure of a man, darmok, inner light and cause and effect
DS9 - deep space nine - my favorite, the story of the dominion war and the fate of cardasaia. It has a slow start but really picks up
Eps - duet and in the pale moonlight
VOY - voyager - I'm not a fan but it's popular, jerri Ryan and Robert Picardo are the best parts of the show
Eps - year of hell pts 1&2
ENT - enterprise - it's been a long road getting from there to here, but your time is finally here. It's campy and bad, but I love it. Go in with low expectations and come out with a love of Shran.
Eps - not going up suggest any, quality tends to trend upwards over the course of the show, but there isn't any one episode that highlights anything good about the show.
DISCO - discovery - the start of nutrek. It isn't as bad as some people say, but it isn't great. There are some good characters, I like Tilly, some neat twists and callbacks (Lorka) but on a whole it's just meh.
Eps - none for DISCO every episode builds towards a season arc pretty directly, so it's not good to watch out of order
Picard - it's bad. Season 3 is better if you are a big fan of TNG, DS9 and VOY, as an entry point it's awful.
Eps - I didn't enjoy any enough to recommend
LD - lower decks - funny animated star Trek. I think it's great, but very referential to old series. Not a good jumping on point.
Eps - wej Duj and much ado about Boimler
SNW - strange new worlds - still running and great. An excellent jumping on point, pretty and well acted
Eps - ad astra per aspera and the Elysian Kingdom