I started with Voyager way back in the day because that’s what was on TV at the time. I picked it up just fine. There isn’t really a wrong way to start watching. If you just jump in wherever, at most you might miss out on some Easter eggs or on the impact of some callbacks, but for the most part the idea of Star Trek is so infused in pop culture you’ll pick up most of it.

I love TOS, but it seems like a major chunk of Trek fandom has either skipped it or only watched an episode or two. If you want to get to know the TOS characters but can’t get into the show, start with the second Star Trek movie and watch through the 6th movie before starting on TNG.

TNG starts out pretty rough. It has some issues finding it’s voice, with many initial episodes being recycled or heavily inspired by TOS episodes. It has good early episodes, but often feels “off”. Good episodes throughout the first two seasons, but it becomes consistently solid in the third. TNG set the baseline for modern Trek.

DS9 comes after TNG. It’s very good right from the start, although it really, really gets good when the more overarching storylines pick up.

Voyager starts part way through DS9, but it really does it’s own thing.

ENT is a prequel. People are ultra harsh on the first two seasons, which I think is somewhat overkill. The first two seasons have some bad episodes, some good episodes and a good number of “meh”. Season 3 is an attempt at grimdark Star Trek, which is a divisive taste. Season 4 is genuinely really great. The writers finally figured out their niche.