To my knowledge, you can only buy weapon upgrades. I have yet to see a weapon in a store. You can find weapons, have them given to you, or get them over the Cerberus Network.
You don't really get new weapon categories. Here are the only categories:
Heavy Pistol (2)
Machine Pistol (2)
Assault Rifle (4)
Sniper Rifle (3)
Shotgun (3)
Heavy Gun (5)
The numbers tell how many guns there are in each category. These don't count the guns you get through the Cerberus Network, as I don't have it.
Most of them are pretty easy to fine with the exception of the Geth Pulse Rifle (Assault Rifle). This is gotten at the end of the
Spoiler: Tali Recruitment Mission. When you get into the room where Tali is, if you are on Hardcore or Insane difficulty, the rifle will be there right after you go inside, if you aren't on either of those difficulties, it won't be there.
click to reveal
It's impossible for any character to get every weapon in the game on a single character. Why? Well, the class that has the most weapon specializations (Soldier) still doesn't have all of them, as it is lacking the Machine Pistol category. Even if it wasn't there's still a point where you get to pick to gain a specialization in Assault Rifles, Shotguns, or Sniper Rifles (If you don't have it already), and one new weapon for any one of those categories if you already have it.
tl;dr - You can't buy weapons, you can't get extra weapon specializations.
Wanna listen to me rant about stuff? I started a blog!
https://theloonybinblog.wordpress.com/