Preferably in a place you’ll remember
I’ve really gotten used to new-school game design.
Whenever I play a lengthy RPG, my mind immediately goes to “I need to find the bank so I can store all of these cool items.” I went through around 15 hours of The Outer Worlds before finally realizing: “oh, the world is my bank.”
Don’t make the same mistake! As soon as you get to your ship/hub (roughly 15 minutes in), use the lockers near the front door to easily store some of your key items. Naturally any stash point will do, that’s just one you’re going to be fast traveling to a lot.
If you want to store stuff: basically, go up to the storage unit you want to place your stuff in, and move until a menu comes up. Press Triangle/Y to initiate a transfer, then a new menu will pop up. Store away!
You can store whatever you want, but as highlighted in the header image, I recommend putting big five weight plus items in there for when you need them. Alternatively, as soon as you leave your ship you can take companions with you to increase your weight capacity, or opt for extra weight perks. Good luck storing the millions of items you’ll come across!