Please don't take this as negative, but I want to give you some counter-arguments for things to be aware of. These are just problems you're likely going to run across in your development, and things that will need to be thought about early.
First) You stand to alienate some players by taking away the choice of who they can play as (until you beat the game). If people replay it, they'll likely feel like that's how it should have been all along. I'd say keep the lottery-style stuff, but have it pertain to something else. Maybe a powerup you get to bring with you, etc.
Second) Level-based progression is fine, just remember that you're multiplying the amount of work you'll need to do. Particularly since you have 3 full characters to fully animate. That crap adds up.
Third) You say that completing the game unlocks the player you beat it with... but you don't get to choose that player to start with. What if the player is forced to complete the game with the one character they DON'T like. Then their only option on subsequent plays is to randomize or pick their least-favorite choice. I would try to find some way around this to make it more inviting to the player Things like that will increase the number of players you get, especially return players. And if someone dislikes choice being taken from them at the start, it will influence how they view the rest of the game.
Please don't take this as a deterrent, but as constructive feedback for you to build on. Also, ideas are important, but execution is the real winner.