What are some "essentials" that you'd recommend every Sailor having with them prior to deployment?

Bring enough consumables to last 6 months. Soap, razors, shaving cream, cigarettes, lighter fluid, etc. use the ships store when you can, expect to be stationed outside the Unrep ship circle which means the ships store runs out of supplies. Have at least 7 underway uniforms including socks ( it still fascinates me that it can take up to 4 months to get something back from laundry.) 5 towels and always keep a spare set of undergarments. If your a Boatswain Mate have a Dress Uniform dry cleaned and ready to go at all times. Not the one you normally wear on watch.

Ability to swim...

If your a smoker or a dipper then you might want to stock up on smokes and dip. They do well on keeping a good supply on ship, but the prices in the store fluctuate depending on how much they have left. The ship may run out as well, and then you can make your money back from your less prepared ship mates.

Make sure you don't leave anything out without someone you trust in your aisle. Even the most redundant things get stolen, I lost my towel that way.

A good attitude VC and life preserver

I would emphasize those things that will make you the most comfortable. If there is a particular soap/body wash/shampoo that you like, bring a supply. Invest in some nice soft towels and a comfortable robe. A nice, warm blanket and high thread count sheets/pillow case. I brought a stainless steel (not glass! learned that the hard way) BODUM french press to make my own coffee. My aunt was able to set up a supply of Starbucks ground coffee that arrived every 2 months.

Ship life is hard. Anything that you can bring that makes it a little more bearable (and is withing regulation) and brings some creature comfort is recommended.