To change the menu, character select and all music in general, you must first have enough VP (Vault Point) to purchase the songs from the Vault.
The Vault is located in Single Player>Vault.
From here, simply purchase the song desired, in my case, it's the original music by Infinite (dope.)
After purchasing the song, simply hit Triangle (or Y on 360 or the appropriate button coresponding to the said change) to set song either globally, meaning it effects the in game music as well, or to the main screens.
Many thanks to Jeff TheSuit for finding this out. No more annoying generic trance/hip hop music for the main theme, and no more generic rap for the character select song!