Never trained at PSA, but here's my suggestion for packing:
Suitcase:
-standard toiletries
-5-7 days of clothing (business casual)
-2 casual outfits
-1 workout attire (if that's your thing)
Backpack/flight case to carry training items:
-1 notebook
-pens/pencils/highlighters
-index cards to make flashcards
-scotch tape
-other "training" supplies you deem essential
Other items:
-Passport
-Logbook (most recent one should do, unless otherwise instructed)
Flight gear can probably be left at home, unless you're flying in from the far reaches of the country. You'll most likely get at least one chance to go home for it before OE. You probably wont need it for training, since the company should be supplying you with everything you'll need for the simulator.