We have been 5 times on the PG, most recently in November and there are no formal nights. There is the traditional Captain's welcome aboard party but the dress is still casual. There were a few men in sports coats and I have seen women in a nice dress, however, the beauty of the PG is you can be as casual as you want as long as you don't wear jeans or shorts to dinner. I think Jim's list is exceptional. The only thing I might add is some sort of beach bag (I use a back pack) to carry your towel, sunscreen, hat, watch, etc. I agree with MarnaLou that the water shoes are an absolute essential.
I think the first time we went we took 2 large suitcases plus a carryon. I don't think we wore 50% of what we took. In November we took one suitcase and our dive bag. We didn't even need a carryon and we got along great. I always use a backback as my handbag so it can carry bottled water, passports, sunglasses, etc. and don't even take a purse.