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.