Get on the siprnet, go to comsublant or comsubpac's website, and search for COMSUBFORINST 5400.XX - Submarine Organization and Regulations Manual. They are different for each class of sub, but they will tell you what you are not allowed to have and I think that list is fairly universal. No one has that entire list memorized, so you're not going to get your answer over the internet. Everything not on that list is fair game, with the caveat that personal items must fit in your 2/3 of the rack pan. The Chiefs will find a home somewhere on the boat for stuff like dress uniforms and other official items when you deploy.
If you can't get on siprnet and want the entire list, wait until you get assigned to a ship and ask your Chief.
If you have any specific items in mind, feel free to ask away.
PS: It's been a few years, but when I left the rules against bringing cameras and wifi devices into a classified secret container (e.g. the entire submarine) were not enforced as long as you kept them in strictly in berthing spaces or crew's mess. I'm not sure if that is still the case.
