You start each Run with three weapon slots. The sidearm (your default weapon) will always be with you from the very start and cannot be changed during gameplay. However, you can obtain different sidearm weapons and equip them in the armory between Runs.

Other weapons are randomly dropped during each stage. When a weapon is dropped in the arena, it will be highlighted. Weapons can differ not only in types, but also in rarity. Get closer to a weapon to see its characteristics and equip it. If all of your weapon slots are full, equipping a new one will drop the weapon that's currently equipped.