First House: Black Eagles - As a person whose previous favorite lord was Micaiah, I thought Edelgard was going to be the most interesting lord going in, and I still believe so. Claude was so very tempting though.
Favorite Black Eagle: Petra - I was extremely excited for her before launch due to her design, supposed myrmidon archetype and Faye Mata VA, but I was also worried that they would play way too much into the "foreigner who not speak language good" trope and relegate her to a comic relief character. Thankfully it's relatively subdued in her supports, and instead she has a wide variety of conversations that paint her to be an interesting character; from curious student under Linhardt and Ashe, to capable mentor for Ferdinand and Caspar, from earnest and unassuming with Ignatz, to cheeky and playful with Claude, to straight up badass with Hubert. She always strives to connect with others and to emphasize their similarities. I find that she is generally not the central focus of her supports and really lets her conversational partner grow or shine. That being said, she herself admittedly doesn't have the most character growth, but I think it's fine since given her backstory and her wisdom, the bulk of that growth must have happened before we come into the picture. At the end of the day, I still find her the most interesting character in 3H in conjunction with best aesthetics (post time skip design whew) and amazing gameplay performance, so fairly simple vote for me.
Honorable mentions: Edelgard, Dorothea, Caspar, Ferdinand — I do like Black Eagles a lot
Favorite Blue Lion: Felix - People above already explained it better than I can. Great character. I normally hate the tsundere archetype, with the only previous exception being Kurisu in Steins;Gate, but Felix has also given it a breath of fresh air for me. Felix x Dorothea A+ support gives me life.
Honorable mention: Annette is the best girl in BL, no need to change my mind
Favorite Golden Deer: Claude - He's a hella good looking, funny, charming guy. No one else in GD really holds a candle to be frank.
Honorable mention: Leonie, given that you delete her Byleth support from existence.
Favorite Other: Shamir - She also caught my eye pre-launch. Stoic and cool as a cucumber, fair enough in my books. Honestly most of the other characters I've found decent but not super compelling; but I do want to give a shoutout to Manuela for her absolutely incredible voice acting from Veronica Taylor.