Star Trek

I personally think that they're all worth watching, but it is worth keeping in mind that they're mostly built to appeal to different audiences, so they're not all everyone's cup of tea (and some of them have/had production issues that did them no favours).

The idea of the current age of Trek being "Trek for everyone", so that instead of the same show and concepts being repeated, there would be different shows, trying their own things, aiming for different audiences.

Discovery, for example, seems to have been aimed more for people coming off of the 2009 movies/contemporary sci-fi, which has a bit more in the way of melodrama, and action. It also seems to have been something of an experimental testing ground for what Trek could be, since the show tried all sorts of things.

Meanwhile, Lower Decks is aimed for older fans who want something lighter, with its heavy doses of references to older Trek, and much more comedic style.

Prodigy was aimed at a younger audience, letting them get into Trek on their own terms, with a modern show, compared to the Funimation-based TAS, which is much more dated.

Picard seems to be a bit for "passing the torch", as it were (basically a repeat of what Enterprise tried, but in a slightly better way), as a way to integrate both the prior Trek series, and the current ones into one smoother, cohesive whole, opening up potential issues, and setting the ground for new concepts, that later series can dive into.

Strange New Worlds is basically a modern take on "RetroTrek", putting down a Captain of the Enterprise, and the standard 5-year mission-type plots, and is probably for people who wanted more of the old shows, but with modern effects and things instead.

Almost all series of the third generation are serialized, so it's harder to just watch episodes separately. Most are best watched one after the other.

• I'm not the biggest fan of Discovery, but still I think that most fans are too harsh with it. It's not the best Trek, but it has its moments and grew better and better. I wouldn't advise to begin with that, though.
• Picard was good. The first season is maybe a little too unoriginal, but I'd say that it's a very solid season until the second half of the last episode. The second season is good, and the third is a nostalgia fest (and I loved every second of it). It may be a good entry point.
• Lower Decks is fun and offer a very different point of view on Star Trek lore. If you like "classic" Trek but are ready to gently mock it, watch it first. I'm in love with this show.
• Prodigy is for children, and its noticeable. It's a good show, but still, a good show for children. If that doesn't bother you, go for it, but pass if it's not the case.
• Strange New Worlds is the best one. Simply that. It would be my advice, and, as the show is almost episodic, you can watch it taking your time.

I'd also recommend watching The Orville, although not Star Trek, but very star trekky.

I know there was some occasional friction between the fans on the old site, but I'll also throw in a recommendation for The Orville as modern Trek that's worth seeing. It does a great job capturing the spirit of the second-gen era presented for the current gen, with its cautious optimism pricked once a week by reminders of challenges yet to be resolved.

The first season is slightly rough (more proof it's a real Trek show?), as they figured out the ratio of comedy to drama, but by season three it's about as jokey as TNG. Fox did a bad job promoting it, it's definitely not Family Guy in space, which I think was probably what the network wanted it to be.

There's tons of Trek people both behind and in front of the camera, so while there's obviously no ties to the Trek canon, it's the closest anything has ever come, stylistically.

Both Discovery and Picard are good series. Both have ups and downs. They’re different from each other and scratch a different itch.

Other than that, I haven’t seen any of the other new series, like Lower Decks.

@dumples I enjoyed the first season of Strange New Worlds. Also, first episode of the second season was pretty good.

I mean, some of them are inconsistent but they are all good and all of them are very much in the spirit of star trek.

Not Picard, that's for sure. I really wanted to love that show but I could not. It isn't Trek. The storyline and characters are not even remotely Trek. They're hollow, shallow, ill-conceved storys that answer questions by waiving their hands and yelling "Borg!". Don't watch it, you'll regret it. It is beautifully made, but it's all style over sustenance.

For me, SNWs and Lower decks are amazing. I did not like Discovery but that is just me so I won't say you shouldn't like it. Picard the last season was good but the first 2 are meh. Prodigy was really good for what it was (a kid's show) and I am sad it got canceled.

Strange New Worlds episodic nature makes it easy to just drop right in. Technically it starts in Discovery but I think you’ll be just fine without it.

If they dropped the SNW and just called it Star Trek, I’d be okay with that. It’s deserving of the name.