Have you heard of Savage Worlds? Fast! Furious! Fun! is the tagline for this tabletop role-playing game, and it lives up to their claims. If you are looking for a game system that's easy to pick up and play, for whatever genre for the duration, I recommend Savage worlds.
As of this writing, the author has been playing Savage Worlds for a little over four years. and in that time I've played a college student against evil, a privateer sea-captain against Pirates and blood magic, a rogue scholar in a post-apocalyptic, medieval fight against old human technological Horrors, a crooked cop in a twisted New Orleans during the Great Depression, a special agent of occult and historical studies against Cthulhu and Nazi’s during World War II, and now a crass punching crewmate on a Victorian steampunk space ship in a pocket ether universe. And those are just the ones I've played in; and there are many, many more. Several of these were home brewed worlds, that I had a hand in creating.
There are dozens and more of recognized settings and has to be thousands of homebrews and shared settings available. So making your own is encouraged, and there’s even a place to share them.
Their most played worlds are probably Deadlands, East Texas University, 50 Fathoms, Rippers, Weird Wars, and Slipstream. Most of the settings have plot point campaigns, and side stories and missions.
Character creation is a breeze and can be done in 5 minutes if you know what you want. The system uses exploding dice and is fairly easy to pick up. My favorite aspect is the using of Bennies to reroll unwanted results, in most cases.
Advancement is simple; you can raise Attributes, Skills, or take Edges, which are what they sound like, advantages when your character does something in certain circumstances.
As for gameplay, is also as fast as you want it to be. The Gamemaster has many options to choose for story/game flow. Don’t have a lot of time to grind through a bunch of mooks to get to the big baddy? Have the plays describe how they mow through those troops, make some rolls, and see if can pull it off. Or, enjoy the rolling slog of combat? Use a grid map and go turn by turn, enjoying the furious aspect of the game. Whether tactical, strategic, narrative, dramatic, or other; Savage Worlds has it for you.
You can find Savage Worlds at www.peginc.com