What I would suggest is getting a reliable vehicle with both cargo space and towing ability, like a pickup truck or an SUV. Sure, it's not as fun or flashy as a motorcycle, but it'll be a lot more convenient for you in the long run.
Why? Well, it's pretty simple. You're in SC for nine to twelve months, off the bat. NFAS and NPS, right? Then NPTU, which is another six months, either in NY or still in SC. If you're still in SC, that's less of a hassle. But getting all of your crap to NY is somewhat more of a hassle. Hard to sling two seabags and a few boxes of personal gear, a computer and a TV on a motorcycle, after all. And your buddies are probably gonna be full-up in their POV's.
Not to mention, down in SC, it rains all the bloody time, which isn't always good riding weather. Up in NY, late spring/summer/early fall is fine, but then the snow hits and you're gonna want something enclosed.
Then look at your choice of duty stations, for worst case weather.
Washington (Bangor, Everett) - Snow, rain.
Hawaii (Pearl Harbor) - Rain.
California (San Diego) - Rain.
Georgia (King's Bay) - Snow(?), rain.
Virginia (Newport News) - Snow, rain.
Connecticut (Groton) - Snow, rain.
You want something that'll let you get to work reliably and on time, in a safe manner, all year round. And you'll want something that makes moving relatively easy; sure, you can have the Navy ship stuff for you, but that's generally more of a hassle than it's worth. Not to mention a DITY move is generally a little more profitable to do, when you work things out mile-by-mile.
So, in other words, get something that's good, reliable and useful all-year-round, then think about snagging a motorcycle for fun or good-weather commuting after you've got the essentials down. I mean, sure, you can use a motorcycle in inclement weather, but while you might be a 'safe rider,' the other schmucks on the road sure as hell aren't.
Edit - And I totally forgot to actually look at drayer's link. Yeah, the Navy has special rules for motorcyclists, too. Hope you're willing to attend all the motorcycle safety training and get all the special gear the Navy requires for you. Because they will come and bust you for breaking the rules, especially on a student status.