This info is a little dated, mostly because of the uniform changes, I don't know what replaces what and all of that. That being said bring short white socks, not the no-show ones, but long socks take up too much room, yes you read that right.
Before I get too far into this, this list only applies to fast boats, boomers are different, you have lockers and rack pans and all sorts of places to put crap, so that is not much of a worry.
I would have ready 3 coveralls, at least 2 pair of utility pants(or their replacements, like I said I don't know), tennis shoes, 7 pairs of underwear, at least 10 pairs of socks, 7 undershirts, a sleeping bag (not a fluffy one, something small and unobtrusive) and a pillow.
Now, if you are hot-racking it gets a little weird. Since every time I hotracked it seemed like wherever my shower stuff was is where there was somebody sleeping, I recommend the following.
2 sets of all of this:
body wash
shampoo
toothpaste
toothbrush
shower shoes-get a $1.99 pair as a backup from the NEX because you NEVER EVER EVER EVER want to even think about taking the chance of considering possibly wanting to ponder the thought of walking around barefoot.
2 towels
1 razor and cream
and 1 each of facewash, lotion, etc that you may need.
I also recommend a book or PSP or whatever. Just don't fall behind on stuff and then get caught playing sonic the hedgehog in your rack after you said you were too tired to stand your watch during ORSE because you were up late last night doing a monitored evolution. Sorry, still a little bitter about that one, anger.
Realistically, if you bring a little too much stuff people will make fun of you, then make you put your extra stuff in the torpedo room. But, then you forget that you put your bag down there, then when you decommission the boat 3 years later you find your backpack with a pillow and towels and a couple books in it.
Don't overthink it, just go with the flow and don't worry too much. If people are going underway the day after reporting, the Squadron is failing them miserably, or they are telling you stories to make it seem worse than it really is. There are at least 3 days of crap to do with squadron and medical and stuff before you even go to the boat. If your POC at Squadron isn't a douchetard, you will know a couple days in advance no matter what. If nobody knows, find harbor ops and tell them you are reporting to whatever boat and you want to know if you should pack a seabag up.
Technically I am pretty sure you are allowed a week of check-in time before going to the boat. So good luck, hope you get the boat that is broken all of the time, and not the one that is filling in for the broken boats.
), and if you go to a boat in the yards or in new con, they'll probably send you out on another boat to qualify which is what we did with several USS Virginia crewmembers back in the day. 
