As others have said, DS9, Lower Decks, TNG, Voyager, are all great choices. Strange New Worlds isn’t bad either.
Now some potential dealbreakers: Lower Decks is a cartoon and heavily references other shows (but does explain most of those references), TNG is very libbed up and side-steps a lot of the moral questions Startrek is known for, Voy solves those questions with warcrimes, SNW tries to be too inoffensive and is very much directed at fans. I can’t think of anything bad to say about DS9.
Sisko intentionally bombed an entire planet into uninhabitability. He’s no stranger to war crimes.
That’s different
spoiler
because he was preventing settlers from colonizing it, he wasn’t actually attacking civilians, just preventing them from colonizing a couple planets.
When they assassinated that Vulcan (no spoilers), that was a pretty good example of Perfidy though.
Is there any order to watch Star Trek in or can I just pick any and roll with it. Will I be missing any important information?
Nah, no order.
When the shows bring in stuff from older shows, they explain it in episode, or you’ll figure out the gist of it from the framing, the writers themselves often hadn’t watched every single episode of the older shows.
I think SNW and LD are the only ones where the writers actually bothered to watch everything.
