I try to find ships that are more geared towards families and also go to places I want to see, then I pick the ship/cruiseline from there. Others may do it a different way. We were recently on RCCL's Explorer of the Seas and that is one ship that is definately geared for family cruising, we had a ball. You honestly can't go wrong with any one of the Voyager class ships.
I'm the family cruise editor at CruiseMates.com (just back from maternity leave) and Donna had good advice to check out our family web site for information on family cruising. Each month I write at least one new article on some aspect of family cruising.
Another good resource is the book "Cruise Vacations with Kids" by Candyce Stapen (Prima Publishing). I helped update the book and it's got lots of information to help you choose the right cruise for your family.
I also answer the family message board Q's so feel free to ask away once you narrow your choices down to a few cruise lines. Perhaps the best article for you to read on the family site is "Kids' facilities and activities by cruise line" that I wrote earlier this year. It's very detailed and gives background on all the major lines offering youth programs.
Have fun in your research!
Luisa Frey Gaynor