I can try, although I wasn't a SWO. My first unit after USCGA was a 210' cutter, so I'd guess the list is similar. I don't know what your homeport situation is, so I'll just touch on the ship part.
Clothing:
- Uniform items. You likely have a ship store, but I always had my main working uniforms and a nicer set for inport duty, tours, etc. If we needed any special uniforms, we were told before we got underway (but typically we didn't need anything special).
- Civilian clothing. This is largely depend on where you're going and how long you'll be out. If we were out during a change of seasons... you would bring the correct clothing. Generally I brought shorts or jeans with flipflops and casual shoes. I'd also bring something a little nicer in case the wardroom went out for dinner. I brought work-out gear, and running shoes, swim trunks and towels. And I brought baseball hats. No matter where we were going I'd always pack a jacket and a hoodie or two.
Now, my ship may have been a little closer than what you're going to, so this may or may not apply to you. For a time I was the Morale Officer, and we would plan things during portcalls (once or twice during a patrol.... guys wanted to do things on their own too). So I would bring what I needed, in addition to whatever the ship hat. I brought my ballglove. I'd bring skates or a jersey, depending on where we'd be.
You'll do laundry, so you don't need too many sets of anything.... except socks and underwear. A fresh set is always good to have.... and some days you'll be working so hard, maybe in some very hot conditions, that it's nice to be clean.
Bring toothpaste, brush, shaver... etc.
And bring things to entertain yourself. You WILL need a break here and there. We would watch movies in the wardroom some nights.... sometimes it was all of the officers, sometimes it wasn't.
I started reading again on my cutter. I got into an author named Ted Bell and my parents got me his books for Christmas (a nice delivery in GTMO one year). If I had to do it all over again, I would have learned an acoustic instrument, and I would have brought it.
Bring CDs and DVDs.
Bring a knife and sunglasses (polarized).
Bring photos from home. Bring something to write with and stamps.
I wouldn't bring anything too valuable or delicate. I wouldn't bring much "USA" stuff. If you're going to a foreign port, you don't want to stand out (although your hair won't help).
That's just a sample. You'll have limited room, but more than you realize, and you'll need to mix it up between what you need for work and what you need for life.