Except for anyone who was there from 1966 on, we all jumped around at the beginning.
I didn't become a Star Trek fan until the beginning of 1991, starting with the movies, and they were in a jumbled order: 4, 1, 5, 2, 3, 6. Doesn't get much more random than that.
I rented "Encounter at Farpoint" but that turned me off from TNG immediately. I didn't watch it until "Unification", which happened to be the same year the first four seasons of TNG went into strip-syndication. So I was watching the old seasons while I started watching the current one. My memory's a little fuzzy on this but I think
the order I watched the TNG seasons in was S3, S4, S1, and S2 with S5 overlapping all the way through. I saw the middle part of S5 before I saw the early part, since I started with "Unification".
In the summer of 1992, I finally got to see some of TOS which instantly became my favorite Star Trek series but it took me about four years to watch all the episodes because broadcast stations kept taking it on and off the air and showing it during late night or overnight hours. Overlapping with TOS, I saw the rest of Star Trek as it was released. Until 1999 anyway, when I stopped watching.
Except for DS9. I didn't regularly watch it until TNG ended. I didn't watch the first two seasons until 1997, so I saw mid-DS9 before I watched early-DS9.
Yeah, so anyway, there was some skipping around. Even today, if I watch an episode on Netflix, I don't stick to any particular order, I just put on what I feel like.
If I stick to an order, it feels too regimented, which is not what I think entertainment should be. If it's serialized then that's different, but most of Star Trek isn't.