I completely disagree with the above advice. You are NOT better off with a cruisetour and anyone who has gone to Alaska independent always sees and does way more than group travelers wasting time waiting for loading and unloading at fixed locations. I doubt the above has traveled independent Alaska??
It is extremely simple to travel Alaska independent. As a sample I would suggest you perhaps consider a round trip rental car from Anchorage and head north to Denali Park for 2 nights, take the Park Road Shuttle to at least Fish Creek. Perhaps spend a night in Talkeetna on the way back? Then depending on your interests, head to Fairbanks for a couple days or go across the Glenn to Valdez for a couple days. Take the ferry Valdez to Whittier. Back to Anchorage, turn in the car, then take the train Anchoage to Seward, you can have a long day and a late embarkment onto your ship or go the day prior and overnight. Key activity here is a Kenai Fjords boat trip, don't miss it.
With only a week, I would suggest only the above train trip, it is the most scenic of the entire line. Taking the train Denali Park/Anchorage is slow and misses everything in between. It also parallels the Park Highway most of the trip, so essentially the same scenery from a car.
Do your homework, and know areas and distances, allow enough time at destinations- a big problem with cruisetours. Consider staying in some great B&B's an excellent way to get in touch with Alaska.