Let's go! I'm gonna split this up into favorite male and female from each cast of characters. I also have not played Thracia or the original Gaiden. A second note, I haven't played the Archanea games enough for me to really pick solid favorites
Jugdral Gen 1 Male- Levin: Holsety!!! Probably the best unit in the game and not even mounted.
Jugdral Gen 1 Female- Tiltyu: She's a sort of Est archetype, but she's super fun to use and a super fun character.
Jugdral Gen 2 Male- Ares: A badass, and he has his own sword to make it even more so.
Judgral Gen 2 Female- Teeny: Pretty much the same as her mother, and I always have her as Levin's daughter and she's awesome.
Elibe (FE6) Male- MAN OF STEEL/Dieck: A God among men. Possibly my favorite in any FE game.
Elibe (FE6) Female- Shanna: The early pegasus knight is always good, and Shanna is not only good, but just a really fun character to get to know.
Elibe (FE7) Male- Heath: Just take a look at his hair and disagree with me. You can't.
Elibe (FE7) Female- Fiora: don't really have a great reason, I've always liked her and she's always been really good.
Magvel Male- Joshua: Not only a 10/10 unit, but one of the deepest characters in SS and FE in general. There's so much there and it's really cool.
Magvel Female- L'Arachel: She's hilarious!
Tellius Male- Gatrie: I've always loved the flirty characters, and Gatrie is the funniest of all. He's a really cool guy, a great unit, and an awesome character.
Tellius Female- Astrid: I like her a lot because of how different she is from Gatrie. It makes their interactions so real, and their supports are some of my favorite in the game.
Ylisse Male- Inigo: Pretty much what I said about Gatrie, but I also have a special connection to Inigo because he's always my son in game.
Ylisse Female- Olivia: I kinda hate saying this, but she is really cute. She's also really nice, and can be quite a force to reckon with if you train her right.
Hoshido Male- Saizo: He's a badass ninja! And he's shouty! Seriously, Saizo is pretty badass, and he's a fun character as well.
Hoshido Female- Orochi: I actually like how eccentric she is, and she's a great mage as well.
Nohr Male- Niles: He's a more anti-hero type character, and that's a cool thing in a game where the story leaves much to be desired.
Nohr Female- Flora: A tragic character for sure, but with hidden depths. I'm not a huge fan of the avatar in this game, but their supports with Flora are actually pretty nice.
Valentia Male- Saber: He's absolutely outstanding, he's ridiculously strong, has an amazing character arc, and he actually takes a role in the story! Also, he looks cool.
Valentia Female- Delthea: I originally didn't care about her, then I started training her and loved her. She's my best unit, and a delightful character to boot.