Well, you typically do nothing in GTA games in the first few hours as it lays down the players, the tone, and the setting. SA was no different in this regard for example.
You don't even get your first gun until a ways into GTAIV, if I remember. In GTAIII, you can't buy guns until like 7-8 missions in. They've always done this. Vice City and old top down games are the main exceptions. In Vice, you unlock guns on the third mission.