Here are a few of my opinions on the matter.
1. Hawaii is beautiful, one of the best cruising destinations on earth. But it's a port-intensive itinerary -- you're in port all day long, even spend two nights in port on Norwegian Cruise Lines' itinerary. If you want more time aboard ship, I recommend the Caribbean.
2. Absolutely seven days or more. Shorter voyages are too brief.
3. You can find a nice ship within the budget you cited, perhaps with a balcony cabin. It just takes some looking around to see the best deals on the ship, departure date you eventually decide.
4. Personally, I like leaving from Ft. Lauderdale the best. The best ships sail from there, it's a ten minute ride from the airport to the pier.
5. In the past two years, hurricanes have fouled up cruises from August to early December and according to the weather experts, this is going to continue for some time. The best deals are right after the New Year's cruise, in January. I suggest avoiding Spring Break, because ships are full of kids. Between Easter and school vacation, there are better prices as well.
6. A cruise is an excellent choice. I recommend Celebrity Cruises' which has beautiful, classy ships with good food and service. Princess is also a good choice. Carnival's newer ships are very good as well in terms of food, service, cabin size, entertainment. Royal Caribbean's ships are lovely, but there are so many complaints about the quality of food.
7. You forgot a terrific travel agent. Ask folks on this board to send you recommendations for travel agents they've personally used and had the best experiences with. We can't post names of agents on these boards, but we can send you recommendations.
I think you're doing a terrific job in researching ships. And, I hope you get everything you need to know here.