I usually play with male avatars, so M!Byleth for me.
I had to learn how to like F!Byleth, tbh. Her design is ... terrible. (yes, everything that people already complained about - the funky leggings, belly showing, and in particular that weird accessory that connects her neck and chest... thank god for the Academy outfit). Not only that, but imo, the previous avatars felt unique from each other. In this case, it seems like they forgot to create F!Byleth at the last minute, so they just decide to grab M!Byleth's face, and then put bigger eyes and longer hair and call it a day. It threw me off a little bit, but nowadays I am cool with it, it was just that I was used for the avatars to look more different between each other, you know? I just fear that if we get another Fe game with an avatar, they will create another skimpy female version.
For the supports... yeah, it sucks that you can't S support Dimitri and Claude as Bylad (like, come on, game, at least the lords!!!). But, if you don't count the students, Shamir and Catherine are great options.