We took our son when he was 2 and 3. We are going again in April (he'll be 4 1/2). If yours are early risers like mine, I would go to the park first thing in the morning. Stay through lunch then head back to the room. Rest, nap or freshen up, then head back to the parks for the evening. We sometimes take an hour or two to just rest then we are good for the rest of the day.
Make sure to take a break if your kids are tired. You won't get to everything and there is no sense in trying. The first trip we took the umbrella stroller. It was fine, but was still a pain on the bus, even though it is small. A lot of people will tell you to bring your own. I would suggest renting a double stroller so the 2 younger ones can ride. Its soo easy to do and our son never complained about the comfort. Our son didn't nap in it since we went back to the room for a break. More than likely, if they are falling asleep, its time to head back for a break, IMHO. If you have 3 kids and take your own stroller, it would be difficult getting on and off the buses with the kids and the stroller. If you happen to stay at a park til closing, it can get very crowded on the buses. Its just something to consider.
If you do rent or bring your own, make sure to mark yours where you can identify it. In the sea of strollers, it can become difficult to id your own. We mark ours with bright fabric.
I would also suggest taking your kids for walks prior to going. The walk from your room to the bus location can be long. We start with short walks and work our way up til our trip.
Hope this helps! There is nothing like seeing your kids faces when they see WDW for the first time! Its wonderful!!!