I doubt all of them are there for no reason. Keiko was a botanist, I'm sure other civilians onboard work with the crew as well. Maybe marrying someone in the fleet is a cheat code to get on a ship without having to join lol
I agree with the others saying start with TNG season 1. Just know, some of the episodes are rough. They took a little while to find their feet. Check episode ratings on review sites, if you want to avoid the bad ones.
I've recently started getting a friend into Trek myself. They're more into DS9, because they've been seeing memes about the Bell Riots, so we've been taking it slow on the other series. We decided to do a Best Of for TNG to begin with. So far, we watched episodes 1 and 2, Encounter at Farpoint, as well as episode 12, Datalore. Then we skipped straight to season 2, and watched episodes 3, 8, 9, 16, and 21. We also watched episode 16, Samaritan Snare, but only because it's relevant to Star Trek: Lower Decks lol
I think Encounter at Farpoint is important for that hopeful view of the future that OP is looking for. It establishes what the Federation is as a power in the Alpha Quadrant, and also gives a nice basic moral hurdle for them to overcome. Plus, seeing Q's first appearance is kinda necessary imo
Lower Decks is my favorite Star Trek since DS9. When it came out though, I was super against it. Didn't think Paramount had any right to be making fun of Star Trek after Discovery season 1. You can tell Lower Decks is made by people that love Star Trek though.
This last season, they did a classic Audience-with-the-Klingon-High-Council episode, and when I saw it, I exclaimed to my fiance, "Yes! I love Klingon bureaucracy episodes!" and then later in the episode, there was almost that exact same line
Strange New Worlds has been finding their feet too. We got a courtroom episode on Augment rights, that really felt Star Trek, and they've had some original stories as well that I've really loved, like Among the Lotus Eaters. There have been a couple episodes I haven't been a fan of, but what Star Trek hasn't had those?
If you're open to it, I recommend giving both shows another chance!
Telarite diplomacy