Could do a HoTS type system where you get tons of fight money upfront as you complete tutorials and such so you have enough to get the bew character after a few online matches and story mode and after you exhaust the easy money you have to grind for hours to get a character.But you'd still have to grind like there's no tomorrow for said characters (or pay for them as the easy way out).
Or, something like Guilty Gear where the DLC charcter is free for the first week(s). With something like you have to play an online match so they can verify you at least own a copy of the game.