Well I don't think I can pick a favourite from every race, but here are a few that I love.
Deku - Deku Butler
I like this character because of his story, and how sad it is. Most of the characters in the game, assuming you complete the notebook, end up having a happy ending. But this guy's story concludes with him crying at the sight of his dead son. I also like that he possesses a spiritual connection with Link, as Link actually bears the spirit of the Deku Butler's dead son in the form of a mask, which was used by the Skull Kid to turn Link into a Deku after the murder of the Deku Butler's son. It's a fairly subtle story, but imo one of the saddest in the series.
Goron - Darunia
Darunia is the first big Goron leader that we see in the franchise, and that right there makes him cool. But the main reason I love him is because he goes above and beyond to protect his people, the gorons, and, as a sage, all of Hyrule's people. When the gorons are taken and held captive in the Fire Temple by Volvagia, Darunia goes to the temple by himself, completely unarmed, essentially sacrificing himself in an attempt to save his people. That's true leadership. That's what defines a brilliant leader. Then he awakens as a sage and helps in the final battle against the King of Evil. He also has a deep admiration for Link, even going as far as to name his son after him. He's a great character that I feel many people often overlook as generic.
Zora - Ralis
Ralis's story is similar to the Deku Butler's story, only flipped and less personal. Similar to the Deku Butler's son, Ralis's mother was murdered by the game's villain, in this case Zant (although possibly Ganondorf) while Ralis was on his way to Castle Town, where he gets attacked and essentially comatosed. When he wakes up, he knows nothing of his mother's death, but he can feel her presence with him, which gives him the answers he needs. He then spends the rest of the game standing by the grave of both his mother and father, and helps Link along his quest. It's another really sad story, but in this case, I think the character is a little bit less likable and the story isn't nearly as subtle or heartbreaking.
Rito - Komali
It was a pretty close call between Komali and Medli, but after some thinking, I ultimately picked Komali as my favourite Rito. He's an extremely well developed character who I actually sometimes feel a personal connection to, as I see some real similarities between us. He's got a great personality and becomes really likable after he gets passed his #teenangst phase. He doesn't have a lot of stage presence in the game, but that's OK. We saw just as much of him as we needed so as not to oversaturate his character yet still keep him as a really cool, likable character.
Gerudo - Ganondorf
Need I even explain myself?
Twili - Midna
I could write an entire essay about Midna, but for the purpose of this post, I'll keep it brief. I've stated multiple times in the past that Midna is my favourite companion in the series, while not being my favourite character. She's easily my favourite twili though. Midna was originally the ruler of the Twilight Realm, before she was attacked and corrupted by Zant, the usurper to the throne. Losing her beautiful body and being turned into a small imp, she does everything that she can to overthrow Zant and protect her people. Originally seeming like a self-centred brat, not caring at all about Hyrule, she has some great development over the course of the game and eventually shows to have a deep care towards Hyrule and Link, even going as far as to sacrifice herself to protect Hyrule during the final battle against Ganondorf (which was the spark that reignited her true form). Knowing that having a direct portal to the Twilight Realm would be dangerous for Hyrule, and that the twili and the races of the light cannot coexist, she sacrifices her greatest friendship for the good of the land. She's a really deep character that I feel gets too much hate from people.
Hylian - Link
Cuz he's awesome.
Sheikah - Sheik
I know Sheik was only a disguise used by Zelda to hide from Ganondorf, but I think there is something more to this character. I like to believe that Sheik was once a real character, perhaps one of the ancestors of the Sheikah race, maybe having some sort of connection with Impa (from Skyward Sword). There is certainly a lot of mystery surrounding this character, which I think is really cool. He/she's also a ninja and looks badass af, so that helps.
Ancient Robot - Scrapper
"bzzzzzat Mistress Fi, I love you you're beautiful, Link you're an idiot gtfo"
I know I only named a small number of races, but these are the only ones that include truly standout characters for me.
Special shoutout goes out to Ezlo, who I only excluded because he's not technically a Minish anymore when we meet him, otherwise he'd definitely be on this list.
