Well since the OP's Title is Cruising for Dummies. May I suggest "Cruising for Dummies" By Fodor's. Available at your local Map or Book Store.

Commercialism aside, I would recommend a decent live Travel Agent for your first Cruise. On-Line is great if you know what you are doing, but for a first cruise you really do not know, nor can you really learn about the Ships and Cruise Lines adequately.

That said, the cheapest (7 day) cruises are usually Western Caribbean on Carnival and Royal Caribbean. Expect to pay about $500 to $800 per person (including the kids!) Although I have never cruised them, Costa used to have kids fares at $99 per week. Disney is good for kids but the prices are usually set in stone. One option that many parents may want to consider is Disney's Park/Cruise option. This consists of 3 days at Orlando at the Parks and a 3 day cruise to the Bahamas.

And one more caution. The cruise lines are now REQUIRED to check Passports for all passengers. This includes kids. You used to be able to get by with a Birth Certificate and Drivers License or other Photo ID, but TSA had to get involved.

Hope this helps.