Most favoured:

1) Car Racing.
All cars are unlocked, but cannot be used until you can scrap enough money --makes it realistic.
Parts get unlocked as you tend to race one car repeatedly.
Events = races.
Time Attack: (self training, makes little money)
Rivals (defeat one gangster after another to unlock new events, makes lots of money, slowly unlocks parts)
Streets: (play against opponent, little money, quickly unlocks parts)

Basically like Drag Racing, but better (more cars, parts, accuracy in price and performance, damage??, perhaps a simple 2d for turning??)

2) Monster Fighting --Mecha Wars.
All Mecha are unlocked, but price limitation makes it hard.
Parts for the Mecha get unlocked (armour, core, 2 weapons, helmet, legs, shield, etc)
Events (fights) = can be isometric-view / perpendicular-scroller 2D mode, like this:


Target Practice = practice the mecha, earn little money
Mission = defeat foes (lots of money, slow parts-unlock)
Rivals = fight online (little money, quick parts-unlock)

If you like either idea, let me know and I can help make the content etc but you would need to implement them to a game.