My wife recently started to show an interest in watching Star Trek. Previously she had seen The Wrath of Khan when she was single digits in age and not much else.
So far we have watched some of the first season of TOS and some other key episodes (still need to show her Mirror Mirror and The Trouble with Tribbles for sure, and probably episodes with Pike, which I think is starting to come up for us soon).
We watched a few episodes of TNG, for some reason Paramount through Amazon started us in the middle of season 3 instead of the season 1. She did not like how Wesley is treated on the show (she is a huge fan of Wil).
From there we moved to Voyager and are about half way through the second season. She is liking it, but not a fan of Neelix (I cannot wait to tell her he improves after Kes is gone) because of his jealousy towards anything that interacts with Kes. I have never finished watching all of Voyager myself, I think I am in season 6 or 7.
I watched all of Discovery (I think I finished anyway), the first Season of Picard, most of Strange New Worlds, and some of Lower Decks. Since she has said she wants to watch the new stuff with me I am doing my best to not watch it all so I have some new episodes with her.
At what point would you move from the old stuff to the new stuff to keep someone from being too confused? Or if confusion arises would you go back and watch the old stuff to answer questions? I know we will not watch Picard until we have gotten well into the Borg stuff in Voyager and some episodes of TNG dealing with it.
Ok I know people will say this is weird but watch through Star Trek Enterprise with Captain Archer since that was supposed to be a reboot for Star Trek that pulled in new fans. It explains the origin story of how humans got into space which I think helps a lot of newer watchers ground themselves in the universe easier. Make sure to make fun of it when it gets too absurd and always have a lighter nearby to hold up during the theme song.
Then go through TNG, Voyager and DS9 jumping between them every episode so you move through all three at the same time. I have been watching Star Trek with my gf this way and it is really fun to compare between the shows and it makes the bad episodes of any one particular series less exhausting because you get to take a break from that show.
Whenever you feel like it watch newer trek and catch up on it, I like all of it and some of it is really good.
Sprinkle in TOS episodes as you go, especially when there are direct callbacks to specific episodes (the SNW episode that echoes a TOS episode is a blast to watch right after watching the associated TOS episode they did such a good job).
I have been debating Enterprise, I really enjoyed the show. It was the first ST content that came out when I was an adult and the only series I watched every episode as it aired (save one or two that I missed because I got home late). My wife and I were just married when it released (less than two weeks) and she would sit on the couch and read while I watched it.