Which shows are worth watching?

You won't get this meme but trust me it slaps
- I'm guessing it's talking about non-canon/retconned works, huh?
  
  When the show with the Black lady aired a lot of """longtime fans""" and YouTubers decreed that it was "not canon" because of XYZ...
  
  Oh, this definitely includes Renegades 👌
  https://en.m.wikipedia.org/wiki/Star_Trek:_Renegades

They're all worth watching, if only so you can make your own decisions.

Always striking to me how many Star Trek fans are so dismissive of Star Trek. I know its of it's time, but TOS didn't take its place in history by accident. Wonderful storytelling, iconic characters - absolutely a must to watch, at least to try it out.
Voyager, by comparison, is pretty mid. The writing is super inconsistent and it absolutely squanders its own premise. Notable for Janeway, Seven, and the Doctor, but it's definitely rough going.
But it's still a good watch. The only ones I don't think I could enthusiastically recommend are TAS, Enterprise, and Picard.
- I enjoyed Picard more than I thought I would. Granted, going in with the lowest of expectations helped.

Not totally right. Strange New Worlds, Lower Decks, and Prodigy are all decent as well. TOS is also worth a watch with an episode list, and TAS has a few good ones as well.
Discovery, in my opinion, isn't as bad some say either. It's hardly peak Star Trek, but I've found I enjoy it sometimes. I also have to throw in obligatory Orville suggestion.
As others have set, Lower Decks is not the first show you should watch though - it's more enjoyable after watching everything. Also, both Lower Decks and Prodigy, I'd recommend watching through the first 10 or so episodes before making a judgement - the first few episodes aren't their best. Lower Decks is often funny and at least once a season (from season 2) puts out a masterpiece that belong with the best of Trek. I'd say the top/my favorite LD episodes are (in no particular order):
S1 E8 "Veritas"
S2 E5 "An Embarrassment of Dooplers" (I hate the Dooplers, but everything else about that episode is solid)
S2 E9 "Wej Duj"
S2 E10 "First Contact"
S3 E1 "Grounded"
S3 E5 "Reflections"
S3 E6 "Hear All, Trust Nothing"
S3 E8 "Crisis Point 2: Paradoxus"
S3 E10 “The Stars At Night”
S4 E4 "Something Borrowed, Something Green"
S4 E6 "Parth Ferengi's Heart Palace"
S4 E9 "The Inner Fight"
S4 E10 "Old Friends, New Planets"
S5 E2 "Shades of Green"
S5 E4 "A Farewell to Farms"
S5 E6 "Of Gods and Angles"
S5 E7 "Fully Dilated" (I think there were some things I wish this episode did better, but I still enjofed it.)
S5 E9 "Fissure Quest"
- Just chiming in that lower decks was what really set the snowball running for me (having before only seen first three seaons of disco, first season of picard, some of the tng movies ages ago and the chris pine movies). Even if you dont catch all the references, lower decks is a very enjoyable series and i plan to rewatch it after having seen the other stuff. Did snw first after lower decks and liked that a lot, and currently doing tng and enjoying that a lot.
- You forgot to add S3 E10 The Stars at Night to that list :)
  
  Yes I did, and now I’ve fixed it.
- I don't suppose that (after everything else recommended here) I could just watch those individual episodes you named and skip the rest, huh? Haha. Also, to be fair, the friend who recommended those shows hasn't watched Lower Decks, I think, which does have a high Rotten Tomatoes rating. Thanks for sharing.
  
  Some of the early episodes are important in my opinion but a little rough at times.
  Once you hit season 2, there is rarely a bad episode - they're all at the very least funny, except for "A Mathematically Perfect Redemption", which is just the most brutal form of torture and an experiment in anti-storytelling. .

Strange New Worlds is fantastic. Lower Decks is great too but you will appreciate a lot more if you watch some of the previous series.

Enterprise all the way.
It starts strong with lots human/vulcan conflict and then eases into 2 seasons of TNG-style adventures.
Season 3 is an imperfect masterpiece that ultimately delivers some incredible episodes. This is where Enterprise comes into its own.
Season 4 is more like a collection of 3-parters that sees the crew touch on all the lore they missed in the first 3 seasons. Satisfying but a different vibe.
Highlights include:
Captain Archer feuding with Duras
Dr Phlox improving every episode he appears
Lt Reed vs Major Hayes
Grapplers!
Low points include:
Decontamination
Archer/Tpol tension
Cogenitor episode
The finale
- I particularly liked the way ENT spaced out its story arcs as a series of episodes which can stand alone but hit on a recurring conflict across multiple seasons, season 3 as the glaring exception.

I wouldn't say pale in comparison. Enterprise was really good in my opinion. Lower Decks and Prodigy too, these are a bit different, but have the same spirit I think.
I also rewatch The Original Series episodes every once in a while. The show as a whole is not really good by modern standards, but it has gems and it's interesting to see where it all began.
Every show except Discovery has a balance of great episodes, filler episodes, and bad episodes. Discovery was bad from A to Z.

Whoever gave you that advice has sound judgement and good taste.
I'd say start with TNG. DS9 is probably objectively "the best", but I think TNG is a better "entry point" if that makes sense? I think if I'd started with DS9 before watching TNG, I'd start wishing not too far into DS9 that I'd seen TNG already. Voyager gets some flack, but it's what I have the most nostalgia for.
After Voyager, I think most of the shows are either "for the fans" (and contain tons of references that only established "fans" are going to get) or... kindof a pale imitation. If you really into Star Trek and run out of TNG, DS9, and Voyager to watch, by all means go on. (I'd probably do TOS next, honestly.) Discovery and Strange New Worlds and Lower Decks are great! But a lot of their charm (Discovery's yet-another-fuck-up-of-Klingons notwithstanding) is about how they tie in to and reference the other shows more so than how they stand on their own.
Enterprise was... not my favorite. It was nice that it answered some questions other series left open, but they spent a lot of the show trying their hardest not to be Star Trek in ways that I say detracted from the experience. I'd say watch it before you watch Lower Decks, but aside from that, I don't think it's really worth watching unless you're that level of fan already.
Oh, and the movies are amazing. Honestly, it might be good to watch the TOS cast movies before moving on from TNG to DS9. My favorite of all the Star Trek movies (and it's not an TOS cast movie) is First Contact.
So, I guess if I were to recommend an order:
TNG
All the movies in release order, though the Chris Pine movies are optional at this point. I'd also skip Section 31 until later.
DS9
Voyager
TOS
Discovery
Section 31
Brave New Worlds
Enterprise
Lower Decks
The Chris Pine movies if you're still in the mood
The Animated Series
Then start watching non-official/non-canon stuff like Star Trek Renegades and Star Trek Continues
Anywhere in that progression that you decide to stop, I'd say you'll have gotten the most impact you could have gotten from the portion you've already watched.
But of course, that's just my take! The other opinions in this thread are all valid as well!

I mean the original series. Yeah its dated but so great. I liked enterprise personally. I was turned off by discoveries first season but I stuck with it and liked the second one. Lower decks cartoon is hilarious. I have not watched any more seasons fo discovery or any other recent content though.

From the new(ish) Star Trek shows I really liked Lower Decks and mostly liked Strange New Worlds and the last season of Picard (you can watch that season on its own, especially if you’ve watched TNG).
I have mixed feelings about Enterprise, but would recommend it as well. It’s only 5 seasons, so …
TV has also changed a lot since the TNG-era, so if you like the vibe of those shows, I’d recommend checking out other sci-fi shows from that time.
All of that is highly subjective of course.
- Lower Decks is great but best saved for last so you get all the references they drop.
- TNG is a bit too slow-paced for me, but I understand that was sort of the culture at the time. Thankfully, for that we've got Jump Cutter, one of the best add-ons to grace browser stores.

Do you prefer story arcs or bottle episodes?
Optimistic or dark stories?
- I know DS9 is considered the "dark stories" one, but it's still bursting with optimism compared with the majority of scifi out there.
- I just go for thought-provoking. TNG S2 has been excellent for the most part (I've started with TNG).
  
  Isn’t “thought provoking“ is kinda the whole point of sci-fi?
  All 3 series have plenty of those, as well as their share of dud episodes. DS9 leans heavier into stories of war/colonialism. VOY is more about survival in desperate circumstances.