I usually like to go the non-lethal route for the start of the game, so I usually just pick up the crossbo from Paul.
My playing style is I like to be stealthy, take my time to watch enemy movements, find a location to hide, sneak up and take them down silently with the baton or riot prod hit to the small of their back. Indeed, and there's also a sniper rifle on the first map, so you can have all 3 weapons to start with before the first map is complete.