Warner Bros Television has done a really good job of introducing characters into the Arrowverse over five years that now it seems like anybody could be added and it would work. But each of the series have a different tone, meaning that certain characters would make more sense on certain series. Here is a look at fan-favorite character I think not only should be brought into the Arrowverse, but which show they should appear on.
My choice for Supergirl may seem like a character better suited for The Flash, being that he is involved in time travel. But I honestly think that Booster Gold makes more sense going up against the Girl of Steel and I think the Flash has done enough with time travel for a while. Booster Gold is a character created by Dan Jurgens and while he does have the heart of a hero, he also wants to have the wallet of a billionaire. The story of Michael Jon Carter and how to escape his poor and dead-end life, he stole items from a superhero exhibit in a museum he was working security at and traveled back in time to make his fortune as a celebrity superhero. Dropping this character into National City and having him start stealing the thunder from Supergirl would be an interesting storyline for both the hero and the reporter side of her. She looks at Superman as the way to be a hero, that is not Booster. The two would butt heads but it could also be a good thing for her to see that deep down, Booster is a hero.
Casting wise I'd go with Austin Butler (The Shannara Chronicles) who has proven that he can play both arrogant and heroic. His series shoots off schedule from most regular series and his co-star, Manu Bennett, can convince him it's a good thing to be part of the Arrowverse. Plus it would be another reference to the Legion of Superheroes flight ring that has been teased in the Arrowverse. Plus being on an alternate Earth, having Rip Hunter's son is till possible.