There you will find email that has not just story tidbits sometime, but literally every level you will be mailed a gun.
Rather, it’s in the “Social” part of the other menu that you would normally use to pause or quit the game.
But it’s not a terminal on your ship, it’s not anywhere in the inventory menu. When you level up, you will constantly be told that you are getting “email” that you need to check. This one was so confusing I actually had to email Gearbox about it during my review process.