August is the big vacation month. Pluses, you will meet lots of Europeans traveling. Minuses, prices and crowds are at their peak. I'd prefer June, it's more comfortable, cheaper and at least slightly less crowded.
We've only taken four cruises. Three with Carnival and one with Princess. The cabins are fine and the food is good. We don't spend much time in our room - just sleep, shower, and change - so we don't mind an inside cabin at all. I'll compare prices and decide if it's worth the extra money to upgrade the room, sometimes the answer is yes and sometimes no.
Carnival is fine. The worst thing about Carnival is the constant sales pitches over the public address system. If you can tune that out, and are educated about what is included in the price of your cruise and what isn't, it's not a big deal - some people hate it.
Princess wasn't significantly different than Carnival. A 600 passenger ship would be a lot different, in both the type of cruising experience and the price.
I prefer ports of call that can be reasonably visited in one day (Tallinn, Estonia is a good example). If you visit a bigger city (Rome, Berlin, London), I agree with the advise to pick one thing and focus on only that. Often the big cities also require a lengthy transportation leg into the city and back, consider that when you think about your available time.
You can really go either way. I usually watch flight and cruise prices, then book them both when I'm satisfied with the deals. Airfare changes more quickly so book that first then book your cruise.
Cruisecritic.com has reviews on every ship, line and port. Although my travel style isn't the same as most of the people on the site, it's good information to help you get a realistic expectation for the cruise.
Vacationstogo.com is an online travel agent that focuses on cruises. We've booked our cruises through them and have had no problems. They have the best search engine for cruises IMO, check them out to compare different options.