Weapons in Wasted are divided into two categories; explosives and guns. There is no way to kill enemies using melee weapons or your fists, so finding a weapon past the starting P30 should be your first priority.
Where can I find weapons?Edit
Weapons can be found in hidden areas, at towns, or at shops. You will spawn at a town if you do not use a Spawn Beacon, so grabbing a gun from a chest at a town you spawn at should be the first thing you do.
M79 Grenade Launcher
Frag Grenade (Planned)