Do the Community Expeditions. They only come around once in a while, and there should be one currently active for a little while longer. You get good stuff with them, and this one in particular is especially good, imo.

Just create a new save. They are set up so that you will get upgrades and inventory slots as you go. When you're done, you can then roll it into a normal save with everything you collected and unlocked. Great way to jumpstart the game and get cool loot!