How did I end up here?
All right, I'm not a big fan of talking, so if you want my story, you had better shut up long enough for me to tell it. I don't have time to repeat myself.

My girlfriend set me up and sent me down for this job we were doing. She got off, I got time. I'd have been in that stinking cell for five-to-ten if our paddy wagon hadn't been stopped during our transport by some friends of one of the passengers, a real stand-up kind of guy name of 8-Ball. So we get out and 8-Ball sets me up with a new place where nobody was gonna find me. He also gave me some new clothes, since jumpsuits aren't exactly the fashion trend of the times.
I was grateful as hell for all the help, but being in Liberty City alone with nothing didn't sound like a way to live. 8-Ball came to my rescue again, and set me up with this guy he knows, Luigi. Serious Mob type. He was real happy to have a guy like me willing to do odd jobs for him, and I was more than happy to get out of the house and do some work. At first, the jobs were kid stuff- picking up some guys, grabbing some cars, delivering a couple of packages, what have you. When Luigi saw that I wasn't screwing up and wasn't talking, that's when I started getting the real jobs, like car bombs and the occasional hit. I got to see 8-Ball every now and then, too. Dude's the go-to guy for explosives. Pretty soon, I was doing such a good job that he recommended me to his friends, like this kid Joey, who runs a- well, maybe I shouldn't say too much about Joey. I don't know you.

Every so often, I'd have to blow off some steam, Liberty City style. Times like that, if I didn't have anything urgent going on, I'd just grab a car off the street, preferably a nice one, a Banshee or a Stallion or something, and just go tearing around town.

Anyway, it went on like this for a while-every few jobs, somebody else would find out about me and hook me up. Liberty City being the place it is, it wasn't long before I found myself in the middle of a full-on gang war between the Mob and the Triads, not to mention some little internal squabbles within the family (for example, I was sent to take care of my old friend Luigi).

Yeah, so that's how I got to the top of the heap. It wasn't honest, but it was plenty of work. After I left the Mob (pretty much had to after all the guys I offed) I got set up with the Yakuza. I did them about the same, and got myself control of most of the city. Pretty sweet.
COMMENTARY
GTA 3 is very violent, indeed. It's not for kids at all. It even says that right on the box!
Anyway, "adult" content is not what made this game a hit, not entirely anyway. The free-form gameplay set in a MASSIVE city environment is the real draw to this game. Should you decide to meet your bosses and take the missions given to you, you can open up more missions, earn more money, gain access to other areas of the city, and advance the plot to your heart's content. However, this is not necessary. Between missions you can just go strike out on your own and explore the city and its possibilities.
Yes, most of the possibilities are crime-based, but it is still a move in a new direction: freedom. Should you grab a taxicab, you'll be given the opportunity to pick up fares for extra money. If you pick up a police car, you can use the radio to track down fleeing felons and "apprehend" them vigilante-style. Pick up a ringing payphone and you may be asked to join the Diablos gang in a friendly street race. You can do stunts around the city to earn a little bonus cash. Or you can always just go on a crime spree and terrorize the pedestrians.
After discovering all the optional activities, some gamers (read: me) never go back to the missions, content to just play.
Gamespot: Grand Theft Auto 3.
http://www.gamespot.com/ps2/adventure/grandtheftauto3/review.html
GTA 3 review. Used to check story details, also screenshots taken from included screenshot archives.
Grand Theft Auto 3 (Game.) Rockstar Games, Sony Playstation 2, 2001.