You'll need quite a few second and third tier items for PoSI equipment. Maniac's Prayers, Inklings of Identity and, especially, Phosphorescent Scarabs are important and kind of annoying to acquire. You'll probably find uses for several thousand Foxfire Candles, especially if you haven't dealt with the Plaster Face. Do you like to treat your Lizard? If so, keep any Beeswax you find. You can generally sell fourth and fifth tier items. Exceptions: components, stuff you need for lodgings or ravens, and three or four Blackmail Material. You'll rarely need Rag Trade or Cartography items other than Glim and a few Silk Scraps.

General stockpiling. Third tier items are interconvertible, so I like to hold onto those. I got a lot of the Antique Mysteries for my Bethlehem reservation that way. Appalling Secrets and lower level Mysteries are very useful, and Jade, Glim and Rostygold get used like pocket change. It's better to sell stuff which can be ground efficiently, like Prisoner's Honey and Mourning Candles, and hang on to stuff which can't, like Souls.