Not really. You'll have an opportunity to purchase anything you'll need at nex.
That can depend entirely on your class team. I saw classes that didn't get NEX trips until a month in, and they were hurting. We had them after admin week, but that's not a guarantee.
Few things that aren't super clear, that I saw make people's life uncomfortable...
Extra underwear. They aren't going to count, and the first couple weeks is rough on trying to do laundry.
Extra socks, especially good comfortable moisture wicking boot socks. So many people ended up with horrifying broken open bloody feet from the issued stuff. Very dumb reason to roll.
Stamps. Always in demand and hard to get on base.
Mouthwash can serve dual function for cleaning your canteens.
Its hard because there is a lot of potentially useful things, but they've been cracking down hard on things like personal cleaning supplies and such. Definately hard to overdo the undergarmets though.
Some classes and people got good use out of a laptop during candio phase, but they seemed to be moving towards banning them when I left. A book for candio phase is probably safer, but it can really depend on your billet.
For others coming along.l obviously, not the OP.