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.

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.

I'd say strange new worlds and the 3rd season of Picard is worth watching. You could try the first few episodes of the rest to see if it's your kind of thing .

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.

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.

Watch Picard Season 3, Strange New Worlds, Lower Decks and possibly Prodigy.

Avoid all of Discovery and the first two seasons of Picard. They are the worst Star Trek has ever been and seem to exist for no other reason than to pander to the “we need to be represented” crowd.