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
Ok, so as a starter, I’d recommend that someone going by the above do a kind of seven episode primer on Star Trek and what it’s about. Moral/Ethical philosophy.
TOS - Balance of Terror, is preemptive aggression ever justified?
TNG - Measure of a Man, what makes a person a person?
DS9 - In The Pale Moonlight, do the ends justify the means?
VOY - I’d go with Equinox parts I & II over Year of Hell, but also a “do the ends justify the means.”
ENT - Judgement, is justice arbitrary or universal?
Skip DISCO, plenty of issues to be examined but each one takes a whole season.
Skip LD, there’s a few issues but they’re not as well presented.
There are good prime directive episodes, but on a whole they just aren’t good intros to the shows.
For example, Pen Pals from TNG has some great moments. The crew indulging Data, everyone knowing Data has an emotional connection with the little alien girl, except Data. Good discussion about the morality of intervention. And a large chunk is Wes being whiny also pretty goofy make up on alien girls hands. It’s good, but not an intro to Trek good.