Strange New Worlds picks up as a spin-off of Discovery Season 2. If there’s one Nu Trek to watch, it’s this.

Discovery and SNW are prequels to TOS. However, Season 1 of Disco is very weak with the exception of one or two episodes. Season 2 is much better and you can probably start here. Then go into S3 or SNW.

Season 3 is where I believe Discovery really shines. It also changes setting entirely. 4 is good too.

Lower Decks takes places shortly after/around DS9/Voy era. So if you’re familiar with 90’s trek, this show is basically like home cooking. You can watch it anytime.

Picard Season 1 and 2 are bad. But if you think of it as non-canon Fan Fiction written by Patrick Stewart, it’s just kinda fun. Season 3 is the final season and is basically the show everyone actually wanted. It’s an epilogue to TNG. There’s a few references to Season 1 and 2, but you can Google the small gaps. You can watch it anytime.

Also, watch The Orville. It’s a love letter to Star Trek, has Trek writers, producers and actors. It’s starts as a dumb comedy that didn’t really know what it’s doing, but by episode 3 they start to find their footing.
Season 2 and 3 and pretty much perfect and IMO as good as the best of Trek. The show gets more serious and the humor takes a backseat to the human element.

The most I'd recommend is:

DIS Seasons 1 and 2 ---> SNW ---> LD ---> PRO ---> PIC ---> DIS Seasons 3 and 4 (these can also be viewed before SNW).

It mostly doesn't matter except for a couple of linking points:

• Strange New Worlds effectively directly follows events of Discovery Season 2 with a plot point introduced in season 2 being a bit of a focus of SNW S1

• It is probably advisable to watch Picard S1 before Discovery S3 and 4 as the first season of Picard introduces lore elements that have relevance.

My suggestion;

• 1. Discovery Seasons 1&2 only.
• 2. Strange New Worlds 1&2 (current).

As for Picard, if you enjoyed the above 4 seasons, I would then watch Star Trek: The Next Generation before Picard as it is a sequel.

The consistency of TNG didn't pick up for me until midway Season 3, now I like it significantly more than Discovery post Season 2.

It doesn't really matter all that much since the shows are spread all over the timeline. There is one exception though: Strange New Worlds is a direct spinoff of Discovery. So you should watch that first. (It's also the show that takes the longest to figure itself out, maybe with the exception of Picard, so it for the most part only goes up from there)

As far as Discovery and forward go, I'd honestly recommend order of release. I'm not going to feed you any "don't watch this, do watch that", I just want to say that various bits of lore are introduced in some series, are then referenced in later episodes of other series. All of the series are making references to each other now. So, I think you get the most of the lore references, if you watch them in release order.

That said, it probably doesn't really matter -- Most of the recent series are in distinctly different places and/or times. Discovery and SNW are the closest (to start) in time and space, and Discovery S2 directly feeds to SNW. Prodigy and Lower Decks are in a similar time space, but very far apart in the galaxy, and Picard starts the farthest ahead in the timeline, though Discovery will overtake it, and Picard also has flashbacks that take place probably close to the time of Lower Decks or Prodigy.

Soooooooooo... overall, probably doesn't matter, but in my opinion, you get the most benefit of lore knowledge in release order.

SNW spins out of DIS season 2, so probably watch that before starting SNW.

Beyond that I wouldn't say there's a strict order, until the recent SNW/LD crossover the rest have been pretty self-contained (almost regrettably so).

I just treat them all as their own continuity. Everything’s so messed up now.

Lol. I think Lemmy would benefit from "categories" of up-votes/down-votes. This comment got my up-vote entirely because I found it amusing.

What do you consider to be "NuTrek"? One issue with the more-recent shows is that they don't have a lot of continuity, to the extent that they would seem to implicitly contradict each-other (and themselves, between seasons)

with that in mind, there's no good "viewing order", as they don't seem to take place in the same world