Great game... truly amazing...
In the beginning of the game you play as your father and fight off a mob group. After you're dad fights a few he gets shot down by the leader and his bodyguards as you watch. That's when it brings you to the customization screen where you can change the size and shape of your body and face and get clothes. That's when you first join the Corleones, a mafia group in New York.
You fight the other enemy mobs throughout this game like the Cuneo and Stracci mobs. You can also buy new guns and pick up new guns as you go through the game and upgrade them when you get the money.
This game has a great storyline and has missions just like GTA would. You can still highjack cars and shoot civilians just like GTA and this is the reason I love it so much. It's a true masterpiece of a game.
I would suggest The Godfather to all GTA fans.