"Officially" smokeless tobacco is not allowed onboard CVN-71 but it is one of the most ignored rules onboard since a fair number of the chiefs and officers use it. Since it is not allowed onboard it is not sold in the ships store.
while it's contraband on, I believe, most (if not all) carriers, its a FANTASTIC way to get checkouts if you are falling behind. I prefer a book (cheaper and easier for me), but it has helped many a sailor get "un dink".
That said, on underways, you really arent gone long enough to need most of the stuff talked about here. Make sure you have
1) plenty of uniforms
2) plenty of pens
3) plenty of toiletries (soap, shampoo, etc), however they do sell generic stuff at the ships stores
4) a personal pillow case (I cant stress this enough)
5) if you dont smoke or dip, dont bring smokes or dip cans... smokers really on each other more then buying stuff
6) laundry detergent, fabric softener sheets
7) stuff to keep you busy at night (movies, magazines, books, etc)

for underways, its not overly important to keep "inspection" quality uniforms ready to go. Have a clean set you can make ready, but most often you wont need it.
last but not least, your sponsor is just that... your sponsor. She will not hesitate to help you out if she is even half way decent. I had a dirt bag for mine, but luckily people in my division helped out a bunch.