Each show has it it's issues for someone to start out with
TOS - Some might be put off by the fact that it is over 50 years old and as such might seem dated by somone viewing it today
Yeah. TOS has some great stuff, but some of the dated stuff grates. Especially the casual sexism.
However, I might recommend the following anyway:
* Balance of Terror
* The Gamesters of Triskeleon
* The Enterprise Incident
* The Tholian Web
* Day of the Dove
TNG - Season 1 and 2 are amongst that series weakest not saying there aren't some good episodes in there but there is a lot of mediocre episodes to wade through. You could start with S3 of TNG and go back to the earlier seasons. Though you might want to watch S2 "Q Who" before the S3 finale of TNG
Seconded!! Starting with "Evolution" and moving forward in chronological order is definitely the way to go.
While S1 and S2 have some good episodes, or episodes with potential, starting with season 3 then going back to 1 & 2 after season 4 might be for the best.
"Contagion", "Q Who", "Elementary Dear Data", "Time Squared", "Peak Performance" from season 2 are easily some good examples. Season 1 is a bizarre mix of the show finding its own feet all while engaging in certain indulgences that only "Encounter at Farpoint" and "Conspiracy" are ones I could suggest off the bat.
DSN - Does use some elements that where introduced in TNG same with VOY which uses some elements which where developed more in TNG but those aren't really essential to know. The thing with DSN is that it is set on a space station but that isn't a bad thing many vote DSN as the best trek series.
DSN also gets its own ship later on, which gives the show a whole new life. They also did stuff on the ship that never got done on TNG, or even could have been done on TNG. I might recommend starting with "Way of the Warrior", finishing seasons 4, then do 2-3, 5-7, 1. 1 is remarkably solid and 2 & 3 are great, but I get the inkling that 4 might be the best place to start.
VOY - As noted above it uses elements used in previous shows but once again not essential to know, this show is similar in style to TOS and TNG.
"Timeless" has too much Borg Technobabble (or "Borgiebabble"), but is a rock solid romp.
I would heartily recommend "Blink of an Eye". For a show that often drowned itself in technobabble and borgiebabble, "Blink" just gets everything right when it comes to engaging high concept sci-fi drama. The story also had influence from TOS' "Wink of an Eye" but does a better job and avoids the obvious plot hole with that trope. (it's the same trope that the original Tron avoided but Tron Legacy quickly fell into as well, about two separate timespans...)
ENT - Once again a show similar in style to TOS, TNG and VOY with the show not really coming in to it's own until S3 and fully using it's prequel status in S4
Yeah, start with S4 for the win - but it is fanservicey at times.
DSC - Well why spoil the surprise in terms of storytelling it's most similar to S3 of ENT and DSN with more long form story telling.
