I haven't finished (or played in a while - lent it to a friend), but my plan is to go with the leader of each house, basically - Claude for Golden Deer, Edelgard for Crimson Flower, etc. Claude is my absolute favorite, though.
Hubert is my favorite Three Houses character aside from Claude and my preferred S Support, but unfortunately he's only available in Edelgard's route. If he was available in the others as well, he'd probably be the one I'd always pick, but hey.
That situation being as it is, and just to keep things fresh and interesting between different playthroughs, I just pick different characters.
I typically play as female Byleth, and in real life I'm asexual or asexual-adjacent, but if I were to seek a relationship with someone I am more inclined toward women. As such, Mercedes and Dorothea are both solid female options since they're bi. If I were to pair female Byleth with a non-Hubert male character, it would probably be Claude, Dedue, Hanneman, or Yuri.
On the rare occasion of playing as male Byleth, my number one choice is Annette. Otherwise I could also see Hapi, Marianne, or Petra. Maybe Edelgard on her route. But honestly kind of a moot point, I think I'm only going to do one male Byleth playthrough, so Annette it is.
Edelgard lol I really enjoy her character so I have a hard time not marrying her She wasn't my first pick during the FE3H reveal, it was Claude, but then I ended up switching to her last minute lol
Claude is next and then Constance! Mostly my top 3.