I know you said that getting a BARGAIN is your first priority, but I really think you should look for a good VALUE. That may not be the cheapest option, but the one that offers the most overall benefit for a given price.

When you do your normal traveling (with your family), do you stay in Ritz-Carltons, Hiltons, Motel 6's, or whatever run-down no-name dive you see a billboard for with a cheap rate? Cruise lines run that gamut as well, and you would be similarly well-served to look at more than simply who has the cheapest fares.

Given all your other considerations, I now recommend Disney Cruise Line. Maybe get a smaller cabin to save a few bucks, but the overall experience sounds like exactly what you're looking for.