Remember your time off the ship is limited. Esp for your first couple of weeks as there will be safety and corporate training and just learning your job. You'll have a couple ports regardless of your line or run that you can pick up extra clothing . . . I'd recommend at least a set of 'thermals' - there are a lot of companies that make very thin ones for running and wearing under jeans. Also whatever jacket you bring, make sure it's water and wind-proof as Alaska can be very windy and rainy.
Check back in this forum for packing threads - you'll find you'll actually use a LOT less that whatever you pack, esp your first contract. You can always have someone mail anything you need to you. Save your suitcase space for what you'll need onboard . . .shoes, formal wear?, computer stuff . . One big suitcase and one carry on . . .
Whatever line you're going to - check on facebook to see if there's a group - you'll get a better packing list . . .