What you have here, is called a premise. It's not a plot, or a story yet, just the beginning of one.
The way I get it - you just want to have a background story, so you can have a reason to start shooting baddies.
Well, that's nice and all, but your story will need some kind of progression between levels.
How about his:
You play a small-time crook who decides to rob a mob-boss to get ahead in life. You get your best friend to help you with the job, since he's already employed as a driver for that mob-boss. At the end of the heist, he betrays you and shoots you, to gain favor with the boss. You drop into a coma.
Years pass. You wake up from your coma, bent on revenge. Your loving girlfriend, who has taken care of you all this time had also took the time to gather all the information you need in order to get to the boss.
In turns out, that during your coma, your best "friend" is not the boss'es right hand man. But in order to get to any of them, you'll have to find them, and the road to them goes through their henchmen, and loyalies.
So you start your journey. You get a gun (or whatever) and goes after the low-level crooks in the mob. As you finish off each of them, they reveal a detail that gets you to your next target, or closer to your real target - the boss, or your friend.
From this point, there's a lot you can do. For example, you could reveal during the final showdown with your "friend" that there was no way out of this, and he shot you and put you in a coma cos that was the only way to save your life (otherwise, you'll both be dead). You can have the girlfriend kidnapped by the mob, when they start getting angry and fearful. There are many options. Let your imagination fly.
Start writing down the story. It may take a while, but it's the basis for your entire game.
Oh, and one last thing: the fact that a story is a cliche doesn't make it bad. Many great games/movies have been based on cliched stories. It's not the premise that counts, but the execution, so don't be discourages if you don't have the MOST original idea.