While modding can be done ahead of any mission and at any Weapon Bench in Mass Effect 3, purchasing upgrades can only be done between missions in the Normandy Shuttle Bay. Shepard can find or purchase and add mods to their weapons, similar to Mass Effect, but they will also need to purchase upgrades for their base weapons to improve its stats, similar to Mass Effect 2.
Mass Effect 3 changes the weapons system somewhat, providing something of a cross between the Mass Effect and Mass Effect 2 systems.
When facing Reapers and other enemies augmented by Reaper tech like Marauders, Cannibals, and Banshees in Mass Effect 3, Shepard and their squad will need the best available weapons.