This is our first cruise and we are going to Alaska. Is it more cost effective to buy the excursions that Princess cruise line offers or purchase them once we get on land?

I would arrange excursions before sailing whether with the cruise line or local companies.
Don't wait until you get there.

Generally they are a bit cheaper from local companies -- however I'd never wait til we arrived. As schmerl says -- you should for sure pre-book any tours.

While excursions booked through the cruise line will mostly cost more they are 'safer'. If you book independently and are late returning to the ship you'll be on your own.

Alaska is so popular with cruisers these days (think over cruising like over tourism) that I recommend that you review the excursions offered by your cruise line to get ideas and then spend lots of time on Goggle looking for local tour guides offering the same (or similar) excursions to compare pricing. An excellent resource to use is Cruise Critic. There is a wealth of knowledge available there.

I would not leave it until you arrive because choice will probably be limited.

Good luck, Judy

Try Chilkoot Charters and Tours in Skagway.

There is a company called Shore Excursions Group who offers slight discounts on cruise excursions but I've not used them.