Exchange materials from salvaging (treasure), don't sell them.
Sell by tab.
Boosters are safe to sell, but they barely net you anything.
Collectables should not be sold.
Core Crystals probably go without saying.
Pouch items can be sold, but it's kind of a waste since you probably bought them.
Aux cores (refined and not) are sellable, you can sell the old/low level ones you have no use for or mass duplicates.
Accessories are good to sell, a lot aren't really all that useful, many get outdated, and you collect a ton of them.
Unused chips are worth selling, unless they give passive bonuses. Those might be worth holding on to.
Cylinders are sellable, but again, you probably bought them.
Treasure should not be sold.
Info and key items can't be sold, AFAIK.