I strongly recommend taking a week in Alaska before/after the cruise. Since you asked the Anchorage question, I'm presuming you have a Whitter/Seward to Vancouver cruise and not a round-trip Vancouver.
This was our first cruise in August 2001, kids were 16 and 12. Kids really loved the independence on the ship; there will be age group progams for both of yours. We were lucky with weather on the cruise, in general June/July is much better than August/September.
We chose Celebrity due to reputation for food, service and kids programs. Only downside is that permits to cruise Glacier Bay are limited, and they all belong to Holland America and Princess, who were the first big cruise lines in Alaska. If you want that, I'd recommend Princess, as Holland America tends to attract a higher age demographic.
Princess also has 4 lodges in Alaska for which they package "cruisetours." They are supposed to be very nice, but will be more expensive for a family of 4 than the rent-a-car, do yourself method we used.
On our own we spent 2 nights outside Denali (you have to reserve bus seats well in advance to spend a day in the park);
1 night Fairbanks (riverboat and gold mine tours);
1 night Talkeetna (cute town, best place for flightseeing Denali, but we lost that to weather, we stopped in Anchorage for a couple of hours at the state museum);
1 night Girdwood (at base of Alyeska ski area, we river rafted class 4+ Six-Mile Creek, includes rental dry suits due to 35 degree water, much better than the more touristy rafting outside Denali);
1 night Seward (visited interesting aquarium, and did all-day glacier and wildlife boat trip in Kenai Fjords);
Our cruise was Friday to Friday, so we went to Whistler for the weekend after the cruise.