You can swap your weapons, and swap weapons with dead enemies/weapon supply boxes using the controls on the right side of the touch screen.
Sniper Rifle (Costs 1,000 XP per mission)
Plasma Pistol (Grunts)
Plasma Repeater (Elites)
Focus Rifle (Major Elites)
Brute Shot (Brutes)
The final weapon, the Brute Shot, will appear on the Operation D Mission 1. You will start a mission with each weapon on the list at least once, but you can also find them all during the game, appearing in the order they're listed in.