In mass effect 2 how do you get different weapons?

I'm an engineer and the only weps I have are shitty submachine pistol that does no damage and a heavy pistol that holds like 20 shots. How can I get better weapons all I've found so far is upgrades for weps that I don't have. I want a shotgun or a rifle of some sort. I'm thinking of going to the citadel and seeing if I can buy any. Lot of info appreciated. I'm new to this game and still learning cuz it's such a massive rpg and I nvr played the first one