I have been going to WDW for years with adults but just recently went with my 2 five year old nephews and 18 month old neice.
We stayed at a house that we rented while we were there and it was great. Our family loved being able to cook our own meals and had our own pool connected to the house.
We did not stay on Disney property that time but it is definitely worth it to do so. There are cabins at Disney's Fort Wilderness. They have a bedroom, bathroom, full kitchen and living room with Murphy bed. They also have a nice deck and grill as well. You could put the kids down for a nap in the room and shut the door and still watch tv or hang out on the deck and not disturb the kids. It has all the usual transportation options to the parks. I believe the cabins are probably your most affordable "suite" like option on Disney property.
Disney also has (as another poster mentioned) a shuttle service from the airport directly to your hotel/resort. I believe it is called Disney's Magical Express. They send you tags for your bags ahead of time and you put these on before you fly. Then they pick up your bags for you and deliver them to your hotel. So you don't need to schlup kids and luggage around at the same time. You then ride in a nice, air-conditioned bus to your Disney resort.
Also, if you don't end up with a room with a kitchen Disney has meal plans. During off-seasons these plans can actually be quite affordable (when I say affordable, please keep in mind that all food and drink in the parks and at the resorts is very expensive so even "affordable" might seem like a lot to you). I've never done one but you pay a certain amount for the plan and then you get 3 meals and a snack (I believe). I would either contact Disney's travel planning group directly (you should be able to get the number on their website) or contact a local travel agent to help you if you are interested in the Magical Express airport shuttle or the meal plan. There are lots of other perks of being a Disney resort guest and they can clue you in. If you want to do any character breakfasts or eat at any of the sit-down restaurants you must make reservations before you go! Really, even at off times these fill up fast and I believe that resort guests might have priority in making reservations.
As for which parks to check out - I would totally skip MGM with little kids - my 5 year old nephews didn't like much there besides the nighttime show (Fantasmic) which might be a bit too scary and loud for your younger children. The Magic Kingdom and Animal Kingdom are the best ones for little kids. At the Magic Kingdom there is a little play area called Pooh's Corner at the back of Fantasyland. This was a life saver! We could sit down in the shade and let the kids just run a bit - there are small water jets back there for them to play in as well if you happen to get one of those beautiful warm February Florida days :o) We just brought a change of clothes for each kid and let them run wild. Even though they get tired at the parks, they had a lot of pent up energy from just standing and waiting for things and this helped. There is usually a convenient popsicle/ice cream concession stand right outside the play area and one of us would run over there and get popsicles for the kids. We would put them in their dry clothes, let them eat their popsicles and then head back out to do more. It was a nice break for all of us. Another tip, Disney allows you to bring in small, soft-sided coolers. We froze some water bottles over night to use as ice packs (and then drank them as they melted throughout the day) and filled our cooler with pb&j sandwiches and lots of liquids (water and capri suns). Disney doesn't have any rules against bringing food and drink in and it lowered our costs and was much more convenient then standing in line for lunch and drinks when the kids were thirsty, hungry and crabby. The kids would actually ask if we were "eating from the cooler today" and they by far preferred that.
A word on Animal Kingdom, this park doesn't stay open very late. They close down before dark because of the animals. So you do want to get there early and try to stay a bit longer then you would at Magic Kingdom because it probably won't be an option to take naps in the afternoon and come back in the evening (like at Magic Kingdom). There is a playground area in the Dinosaur section that might let the kids unwind a bit but if it is sunny and warm there is no shade so we didn't spend a lot of time there.
Hope some of this helps. Don't forget to get your MM ears. There is a little shop on Main Street in Magic Kingdom that still embroiders names on the back of the ears! Have a great time and take lots of pictures!