As far as time of year, it is crazy busy on the holidays... Christmas and Thanksgiving particularly. We've always found the weekdays during the late fall and in early December are good (In December, the Christmas lights are already up at Disney Hollywood Studios (formerly MGM) and they are phenomenal!). Also Jan & Feb tend to be quieter, pre spring break, but a little cooler for weather. These might be tough with a school aged child, though. We are Florida residents, so we have flexibility in that way.
Staying on property is great, and you avoid the parking fees... however, if you book far enough in advance, you can probably get a condo with full kitchen facilities off property for a great rate. You can go grocery shopping and save a ton of money by packing sandwiches for lunch... Disney will allow a small cooler.
The younger 2 children would like Magic Kingdom and Animal Kingdom best, I think, though Epcot recently put in a new play area for the little kids, and we found the seeing the characters there was SO much easier than at MK.
It is tough to spend the whole day at the park for the little ones. If you get a hopper, you could go to one park in the am, come back and relax, and then go to another in the evening. The parks all have child care centers, which are a great place.. quiet, cool... to feed and change the baby and just take a breather if you do decide to try to spend the entire day.
Have fun!