We go every year... My kids go freaking nuts for Disney World...
I think the best time to go is October or November... January or February are pretty great too, but depending on where you're flying in from it kind of sucks to have to worry about weather (not in Florida, but where you're flying in from or over...)
We've stayed at the elite resorts on the monorail (Polynesian, Contemporary and Grand Floridian) and as nice as it is and as convenient as it is, it's not worth the extra money. We loved Port Orleans and Caribbean Beach and both were a lot less expensive. You have to take a bus to the resorts, but they run all the time and are very convenient...
Get the meal plan. If you go in the fall, you can usually get this thrown in for free. Even if you pay for it, it's definitely worth it.
Get a park hopper pass. It gives you flexibility. Some of the parks (usually Animal Kingdom) close earlier than others and then you can go to dinner and then spend a few hours at Epcot before calling it a day. I don't really care for Epcot that much, but going there for two hours two or three times at the end of the day is a lot better than spending a full day there... Keep in mind, my kids are 5 and 6...
Chef Mickey's restaurant is a must if you have kids, especially if they're into meeting the characters, getting autographs etc...
I've heard the Princess character dining at Epcot (some Norwegian place) is awesome, but I haven't been there since I have boys and there wasn't any interest...
We got to see some of New Fantasyland when we were there last year, and it's pretty cool... They have a Beauty and the Beast themed restaurant called "Be Our Guest" that is really, really awesome, no matter what gender or how old you are... The food is insanely good, and it's just really, really classy and nice, but in a way where you're not scared to take the kids there...
As someone else said, go when school is in session....