As far as when to go this again depends on your preference because each month in Alaska seems to hold something different. May and June are considered the driest months, keep in mind you are going to be in some rain forest areas so there may still be rain.
May is great for seeing snow melt providing thousands of waterfalls. The whales will be there but it is still close to the start of whale season. Temps on average should be in the mid 50's to low 60's, of course mother nature does what she wants.
June still has many waterfalls and more whales will be coming in. Closer to the end of June the salmon runs will start and more wildlife will be able to be seen on land such as the bears. The temps will be on average coming into the mid 60's to low 70's.
July the temps will be surprisingly warm to most people, however July will be starting into the rainy months. July will be into the peak whale watching season and the wildlife on land will be more likely to be seen. July will also be coming into mosquito season.
August in the beginning will still be rain season with good temps. The end of August temps will start to go downward but still be decent. There will still be wildlife on the land and plenty of whales.
September of course it will be getting cooler. The whales will still be around but will be starting to head back to the warm waters. September the sales from the shops will be going on so they can close up shop for the winter.
Ultimately the beauty of Alaska is there all cruise season it is just in a constant change.
My personal favorite time to cruise Alaska is anywhere from late May through June. We love to see the waterfalls and see whales. We are from Northern Minnesota so we prefer the temps during this time of year for cruising.
Our personal preference for cruising Alaska is with Princess. We have been on 5 different cruise lines, however Princess so far just seems to be the one that we are most comfortable on. We always feel, as the add says, like we belong on Princess. We have only had one cruise line that we really felt out of place on but we still had a great time due to people we met on the cruise, that cruise line was just not for us. I won't mention the one that we didn't care about because it is just our personal opinion.
As far as ships we prefer in Alaska we always choose the Sun class ships. The one reasons we choose this is we are not big on bigger is better. Actually the Sun class is a little larger than we like but we do enjoy the ships and we have been on them enough that we know some of the better places for viewing of the wildlife and the glaciers when in the fjords.
Like I said you must find what is right for you but you asked my preferences and I have given them to you. We go to Alaska for its beauty both on land and in the sea. Alaska is our favorite place to cruise and even though we do cruise other places it is the one place we will return to over and over. This again is our personal preference.