Okay, here's my approach to packing:
A lot I'm drawing on my experience with the Marines, so I'm hoping things aren't too different with the Navy.
I'm putting things in plastic bags. When I was at Marine OCS we needed plastic bags for humps. You had to put a lot of stuff in your knapsack that you just didn't want to get wet. I don't think there are humps at Navy OCS, but regardless plastic bags are always useful. For example, they say you have to have gouge books all the time. If you're sticking that thing in your pocket or sock it's going to get sweaty and nasty. That's what happened to my Marine gouge book. Well, thee fact that I dropped it in the toilet when I was cleaning didn't help. But anyway, I'd put it in a baggie to keep it dry.
I'll tell you one thing that I'm planning on bringing that I think is essential - Biore face wipes. You're sweating all the time and these things you can just whip out and whipe your face with really quick before doing the next evolution. I say the same thing about those single-package hand whipes and Purell. Bandaids are great as is foot powder, bug spray, and hand lotion if you have room. Some old nylons are the best to shine shoes quickly with. A nail clipper can also help with Irish Penants. Bring like a colorful notebook to write letters in or something. You would be amazed how just that little bit of color can sort of lighten your mood. Notecards if that helps you study. Um, and a permanent marker - in case you need to put your name on your clothes. Sometimes they issue ones that just wash off or fade. I think I'm just going to use spray-in conditioner because it's quicker and with short hair I won't need much anyway.
BUT after all that, I'd pack as lightly as possible because you'll be hauling all that stuff around. As much as you can put in your car I would. I personally would rather do without then get yelled at. I'm not packing like 3 whole months worth of tampons because you'll get a chance to buy more. In fact, I'm doing away with huge bottles shampoo usually comes in and putting what I need in smaller travel size containers because with short hair, I'm just not going to use that much. Econo-size = being able to move faster = less DI in your face.
I don't know about inspections for the Navy. I think the Navy MTT they check everything - foot locker, wall locker, etc. They did that once in the Marines and we hid extra stuff under the trays of our foot lockers. There's trays on top which we all arranged and then underneath is just a huge space for whatever. And we just piled all sorts of stuff in there. Also, I'm sure you get to put stuff in your car or seabag from home if you need a place for extra stuff. But I don't know for sure.
I'm not sure what I will be showing up in. "Appropriate civilian clothes" - that could mean anything. ???
Good luck,
-Becky-