I've had some time to think about this. Ignoring obvious characters from the super popular Nintendo universes, here's the characters I would go with, and why.
Isaac (Binding of Isaac) - Offers the greatest amount of item options, as most items in the game have some synergy with one another.
Travis Touchdown (No More Heroes) - Yes, its another swordsman, but he combines his moveset with wrestling moves, and is very much like a Deadpool type character in that he can break the 4th wall.
Billy/Jimmy (Double Dragon) - Iconic duo of the early days
Yuber (Suikoden 2/3) - Instead of going for Luca Blight who would be another swordsman, I went with his partner in crime Yuber, who while being a knight in Suikoden 2, dons a bowler hat and dual rapier type swords in Suikoden 3 and can play a much faster attacker.
Hero (Lies of P) or Chuck (Dead Rising 2) - The reason I chose these 2 characters are because of the item modification they add to their individual games. The main character from Lies of P can combine parts of weapons together to form new weapons, and Chuck introduced Crafting. While Frank West is the more popular character, Chuck was the protagonist for DR2 which had the crafting mechanic.
Big Daddy (Bioshock) - A slow beefy character, also brings a unique underwater stage in Rapture.
Stages:
Lemmings (Lemmings)
Rapture (Bioshock 1)
Columbia (Bioshock 3)
Estella Opera House (Lies of P)
Krat Central Station or Hotel Krat (Lies of P)
Still Creek (Dead Rising 2: Case Zero (the demo to Dead Rising 2)
Raftfleet (Suikoden 5)
Santa Destroy (No More Heroes)
Crawl Space (Binding of Isaac)
The Beasts Home (Binding of Isaac)