This part of the game is always the most exciting. Yeah, what can I say, I'm a romance lover, so...
Well, as a male character, my first choice would definitely be the most straightforward one in both paths, Nohr and Hoshido: Azura. I just love her design and story-wise, it seems as an excellent match.
However, her aside, I would choose the following:
Male, Nohr: Camilla or Pieri, whether I would be in the sexy or stylish mood. Former more likely than the latter, however. I gave Luna some thought, but she's basically a second Severa. Sakura looks amazing and would be my first choice, but I'm not a siscon... really! I'm not!
Male, Hoshido: I would most likely end up pairing him with Kagerou. She's got that look.
Female, Nohr: Both Odin and Lazward would be good to go, despite the former being a second Owain and the latter a second Inigo.
Female, Hoshido: This one is the hardest. Probably Subaki, with no excessive reasons why.
Huff-puff, looks like I'll have quite a variety if I go with Male, Nohr while quite the opposite if I go with Female, Hoshido. Nice, complete opposites on multiple levels.