Two or three months... wow! Most people on this forum only plan for around ten days, not nearly enough time to see even just a little bit of Alaska. I went for two and a half weeks to Denali, Seward, and Homer and feel like I just skimmed over the places I went.
The first thing I'd recommend is to buy a guidebook. Frommers is always reliable, and I also recommend Alaska by Lonely Planet. It's great for budget travelers or people who are doing it on their own in general. A guidebook gives you a good overview of the different places you can go to in Alaska so you can get in your head what you want to do. Alaska is a huge state, but two or three months just might be able to cover it, at least partially. :)
You'll never see an Alaskan telling you to take a cruise on a Mega ship (Royal Caribbean, Princess, etc), but I don't know about the smaller ones, as they are rarely mentioned in this forum.
Another idea to see the Inside Passage is to hop around from town to town on the Marine Highway, which gives you more freedom to make your own schedule.
My thoughts on Barrow: don't go. I really don't see the point; the little to do up there and the scenery's not amazing. Plus it's not cheap. I would recommend not going much farther North than Fairbanks.
There are two musts for your trip, to go to Seward for a cruise to Kenai Fjords, the Sea Life Center, and Exit Glacier and to spend a few days in Denali, take a bus tour into the park and maybe do some backcountry hiking. Other ideas are to explore Wrangell St. Elias National Park, Homer, Katami National Park and Fairbanks.
Again, Alaska is a huge state and a guidebook can orient you to where you want to spend your time.