I can't help but to feel GTAIII did criminality the best. From the beginning of the game Claude is betrayed and left for dead in a city completely unknown to him. Giving insight into how the criminal underworld you were about to embark into operates. After that Claude is seen using a prison convoy ambush and terrorist attack toward his advantage, subetly indicating to us that quick thinking is pivitol to success in GTAIII. Then after escaping incarceration and playing Mr. Pimp for a brief moment, you're put out into the streets of a city where it's biggest asset is the fact that it has none. If you wanted to acquire a fancy new sports car or a high end M4 rifle? You had to search for it. There wasn't an actual map (radar doesn't count) so you, the player, were forced to scout the city on your own and try to find the quickest routes.
Unlike the succeeding games, in GTAIII's world there were no distractions from being a criminal. The game play itself really focused down on that. More than GTAIV I'd say.
You couldn't hang out with friends and play pool.
You couldn't go base jumping.
There was no deep sea diving.
You couldn't buy new clothes.
In GTAIII's grim grey city, all you had to do was not follow that proverbial train, but rather steal it and use it toward your advantage.