Hi, welcome to Alaska------You didn't mention how much time you have for the trip. That is very important as there are a number of basic itineraries to ponder.
I always encourage first timers to try for two weeks. I also suggest crossing the Gulf of Alaska and doing some of the interior.
There are three basic types of Alaska cruises: 1. The round robin, from either Vancouver BC or Seattle, this type does not cross the Gulf or go to Central Alaska, they only do Alaska's Southeast "Panhandle" and usually go as far north as Skagway then head back south, during which many of the obligatory ports in Alaska's inside passage are visited. About 65% of all Alaskan cruises are of this type and almost all are of a week duration.
2. Cruises which begin or terminate in Seattle or Vancouver or begin or terminate in Anchorage (Note, very few cruise actually visit the Anchorage port, rather they use the more southern ports at Whittier or Seward, if the cruise begins in central Alaska guests fly into Anchorage and if they begin in Seattle or Vancouver they fly home from Anchorage (Note: some guests don't fly back home but return on the ship, which involves a "back to back" booking).
3. Many visitors prefer to cruise to Alaska or cruise from Alaska and spend a week or more on land touring the interior and central Alaska (You won't see the big mountain very well "Denai" or Denali National Park unless you go inland and get away from the coast). They usually do this by renting a car and going it alone or taking one of the popular "cruise tours" offered by a few of the cruise lines serving Alaska.
There are other variations but these three are the basic, give me the time you can spend and I will try to narrow it down.
The most noted major lines serving Alaska are Princess, HAL, RCCL, Celebrity and now Disney, some of the other majors schedule a few cruises up here from time to time. Also, luxury lines like Regent, Silver Seas, Crystal Cruises and Seabourn are seen quite often as well.
By far and away Princess and HAL are the big boys since they made major investments (They own numerous hotels and resorts, tour companies, railroad dome coach cars, coaches, etc here), in Alaska decades ago. As a result both lines get seniority preferences for sailing into Glacier Bay in the National Park there, this is because cruise ships entering the bay are restricted to annual allotments due environmental concerns. The three major glacier viewing, from cruise ships, attractions are Glacier Bay, Tracy Arm and Hubbard Glacier. It is debatable which is the best, I prefer Hubbard Glacier, for glacier calving viewing, but the ship must leave the inside passage and travel about half way north across the Gulf of Alaska to see it. Glacier Bay is definitely preferable to Tracy Arm, unfortunately, since entrance into the Bay is so limited many lines can not get a permit to go there.
Anyway, this gives you a brief glimpse. Here is a link for more: