I've got two shorter recs that focus more on the perspective of the adoptive parent, but they're among my favorites and I don't see them recommended elsewhere in the thread.

I'm Going to See the Folks I Dig has Lily plan for the whole "My sister is a spiteful bitch" thing and makes it so that Remus is the anchor for Harry's blood protection. linkao3(24174466)

Black Wings of Glass features a trans Harry and one of the few portrayals of Snape that I can actually get behind. Severus takes in a young Harry and turns out to be a pretty decent dad. linkao3(9879073)

Lastly, if you can tolerate a WBWL story (although without irredeemable Jily, which is nice) and are alright with a female Harry, I'd recommend Blood and Magic. Harry is ripped away from the Dursleys in a surge of Accidental magic and is stumbled upon by an unlicensed potion seller. This author really likes to explore aspects of magic and the Magical World that Rowling didn't, so this fic features a clever take on the concept of a Necromancer, looks at magical communities outside of Britain, and some exploration of the Founders' Era. Sirius does adopt Harry a few chapters in, which leads to some Pureblood Politics ^TM , but the author avoids the biggest pitfalls of that trope. linkao3(72834471)