First, aloha and welcome!
Can I throw a complete and total wrench in your poll and vote 'none of the above'? - and here's why. To best explain, it's best to discuss why I wouldn't recommend each of the resorts in your poll and then discuss the resort (or resort category) I would recommend.
Pop Century/All Star Sports: These are Disney's version of a Motel 6. They're about as inexpensive as you can get while still staying on Disney property. Pros: they do have all of the perks of Disney properties - the Magical Express, park transportation, extra magic hours, etc. However, the cons: the queues for the busses can get very long, the busses can get extremely crowded, and then the rooms themselves are very small and do not come with ceiling fans or refrigerators (unless you have a medical reason, you have to pay a rental fee for one). The rooms are so small, even though room rate is based on two adults and two children (ages 3-17), I wouldn't want to sleep more than two people in one of those rooms, even of you are only using them to sleep, shower, and store your things.
Art of Animation: I have not stayed there so I cannot in all honesty advise for or against it. However, since I know it is in the same category as Pop and All Stars, I would expect that much of the same pros and cons also apply.
Animal Kingdom Lodge: This is a Deluxe resort and, therefore, one of the most expensive properties Disney offers. If you actually are going to spend time enjoying the property, I would recommend it highly. The property is amazingly themed and beyond gorgeous. If all you are going to do is us it to sleep, shower, and store your things, it'll be a waste of money. Plus, the location isn't close to anything except Animal Kingdom and Blizzard Beach; unless you have a car, you'll have a horrible wait for bus transportation to just about everywhere.
Instead, I would suggest you consider a moderate resort, perhaps Port Orleans French Quarter or Coronado Springs. They're both priced between Pop/Art/All Stars and Animal Kingdom (hence he moderate category), the rooms have ceiling fans and refrigerators standard, are large enough for more than two people to sleep comfortably, the resorts are nice but not so fancy that you feel bad about not spending all day there, so still perfect to sleep, shower, and store your things. I don't know how many people are going with you, but those value rooms can feel crowded after a night or two with even two people. The more people you have, the more space - and sometimes, the more rooms - you will need. French Quarter is very small, with just one bus stop; Coronado is much larger, but I think the rooms are a little nicer. I don't think either option is bad.
Have fun and don't hesitate to ask if you have more questions.