If you want the cheapest options you have the three. You could rent points for a two bedroom, or even book like hotel thru Disney at like SS but that would cost more either way, or you can get a deluxe room at BC, WL and a few others, again expensive, but then again they come with club level access which would be great with that many kids.
As for which would be best, we did AoA one night we did not like it, but that is us kids older, and wanted less in your face theming and more exciting pools. AoA is very kid friendly and probably a good choice for young kids. You have three separate sleeping areas, and you and spouse will have separate room. You will have two bathrooms, and many say you can eat breakfast in room. The pools are just plain no slides and such, but for your younger ones there is a splash pad and wading pool. It is noisy and crowded since it is value, like a motel 6 outdoor corridors and such.
All star music, I have never stayed, personally i don't think it will be as fun for the kids, but maybe. You would have a separate room from the kids, but they would all be together. The bedding is different, ottoman bed, pull out chair and pull out couch. so depending on girls and boys, it may be a better lay out for you, or it may not matter to you. The pools and such would be about the same, although not sure they have a splash pad.
Buses on in both these places I hear is awfully crowded and takes time.
Cabins, you sleep with two kids, oh here is another difference, I know the cabins have a queen bed, the others I think only have full beds. The queen bed is in room with bunk beds, so you would probably need to put youngest on bottom and oldest on top and the other two in the other room on a pull out sofa. You will have a kitchen but no longer has a stove, but a micro. You have a deck and a picnic table so you could eat breakfast and lunch at cabin.
Pros and things to do at cabin, pony rides, carriage rides, wagon rides, archery, horsebackriding. Pool with slide, movies, camp songs with chip and dale, more food options, boat to MK, pole fishing, boating and lots more. Cons, buses, you need to take inservice bus to outservice bus, but you did say you were driving so you have a car.
A deluxe would give you two queen beds and a queen sleeper sofa. It would be in deluxe, balcony, food service , club level.
Is your 3 yo actually three before you go, if not you could have lots of other options, of 5 in a room and one under three in a play and pack. You could do most moderates, I would say POR would be a great one, all moderates have better pools. With that you also could do most deluxe also, not AKL or WL but all others have two queens and a daybed and a play and pack. You also could do many of the DVC studios.
Anyway those are your options, hope that helps. Have a great time.