To unlock new weapons, outfits, and equipment you need to do so through the vendor. The way to unlock them is by receiving vendor points (VP) in battles/missions.
To choose what item type you want to unlock next, select it under the lobby.
As you begin to unlock more items, it will become progressively harder to unlock more with the same amount of work you are putting into unlocking 1 item. In short, more unlocking leads to harder unlocking. Try unlocking 2 items of one type and switch to another.
The next item to unlock is chosen at random. While in the menu, under the progress section, you can see the rarity of each weapon for each class. When a item is unlocked, you will obtain it for free.