In between missions I jump to all the vendor locations(just the ones you don't have to fight to get to them) via fast travel. As the vending machines recycle every 20 minutes, it's quite easy to do. As some of these Legendaries can be quite expensive, you need plenty of money. I got into the habit with BL1&2, of picking up everything and selling. I only keep about 6-7 weapons/items in my backpack.
Wow, I’m the opposite, I always seem to have about 20 guns and I can’t let some of them go. At level 20 I still have a level 7 sniper rifle (it is STILL awesome!) and my first luneshine gun because it looks so good. I know I should let them go, I need the space badly, but I just can’t get rid of them yet, they already have sentimental value. Too much good loot in this game.