Who is better to get in the legendary Banner?

Summer Corrin, Mia, Dorcas, Brave Ike, maybe PA Olivia.

Dorcas, Brave Ike, Olivia, Shiro, and/or Mia (but she's not my favorite, I need someone with bulk)

Shiro, Corrin, Mia, Olivia, Dorcas, olivia, Brave ike, and gaius

Not sure about some of these answers as I doubt you have the orbs to go for as many as they're listing unless you plan on sinking a ton of money into it, which I wouldn't suggest. Keep in mind I'm coming from a competitive standpoint, not a "oh so cool" one.

Tl;Dr: Brave Ike or Dorcas (ur choice), and PA!Olivia

In blue: Summer Corrin really only pulls her weight in a flier emblem team so unless you already have a solid foundation with the likes of New year's azura, Elincia, Cordelia, etc she isn't worth targeting. Shiro is garbage
Don't let his rating on this site fool you, 4/5 may as well be "good sometimes" and his sometimes isn't often enough to justify him over many other infantry lances.

In green: Both Dorcas and Ike fill similar roles as bulky, baity, green infantry. Dorcas has built in distant counter which immediately jumps him to the top priority of many lists. Not to mention you are more likely to have Brave Ike already. B!Ike does have that steady breath though, which if you don't need him, is a staple skill in high end arena.

In red: you said ignore legendaries but I feel it's worth mentioning we are getting a free V!Ike which makes red more unappealing as you could pull duplicates and Warding Breath isn't THAT good compared to it's defense based big brother. Mia is a solid red unit that'll pull her weight but there's just so many red swords you could also use that it isn't worth accidentally pulling the dumpster fire that is Summer Leo instead to get her.

In colorless: Ignore everything and go for PA!Olivia. Gaius sucks. Jaffar sucks even more. It's risky since 2/3 of our units here are bad but Olivia is almost worth it assuming ur willing to risk the orbs. She's seasonal so it's hard enough to get her as is, which increases her desirability but also a dancer. And comes with one of the most unique support sets available making her perhaps the most flexible dancer around.