While the decision on whether to stay at Disney World or stay off site is a significant one, I wanted to put something together about what to do if you make the choice to stay on property.
The easiest first, if you are active or retired military, stay at Shades of Green. The cost to stay here is very cheap compared to most other Disney locations, it's a rather nice hotel with comfortable rooms, and is in close proximity to the luxury hotels, particularly The Polynesian. This is helpful because although it's well-positioned it is not on the monorail line. You can take a short walk over to The Polynesian to get to their monorail, and another longer walk to the travel and transport center (TTC) to take the Epcot monorail.
Of the three luxury "Deluxe" resorts, I rate them Polynesian first, Grand Floridian a close second, and Contemporary a distant third. Each of them have great rooms and the Grand Floridian in particular has a very high class atmosphere. All are located on the monorail line with the Contemporary having the advantage of first stop from the monorail line being the Magic Kingdom. Grand Floridian has the longest monorail loop to get to the Magic Kingdom, but conversely it's not a terrible walk if you just want to follow the sidewalk around the water (I wouldn't recommend this for little kids without strollers!). What makes the Polynesian my top choice is that the rooms are relatively nice with a Rat Pack luxury feel inside (green marble and lots of dark wood veneers) while being generally cheaper than either of the other two Deluxe resorts. Added bonuses are that it is on the water access for boating, has the second fastest monorail time to Magic Kingdom, and the fastest time to Epcot if you walk to the TTC. The kids splash area is pretty good with a large volcano water slide and lots of room in the pools - does not compare to newer splash areas like Coronado, though.
The Contemporary has a neat feature of having the monorail actually come directly into the resort hotel, but the tradeoff here is that the large A-frame tends to be very noisy and has difficulty controlling the environment (both A/C and smells). I'm not sure how anyone could sleep here when the monorail is running. The restaurants we tried in the Contemporary, Chef Mickey and the Wave, were just not good in comparison to your food choices at the other hotels. Slow service, fewer choices, bland... just blech. I've heard it said many times when we are there that the Contemporary is the hotel choice for senior citizens, and I'm not inclined to think that impression is wrong. This is another factor that makes it a bad choice for my loud and rowdy children. The only reason why I don't throw it to the skip list is the monorail, honestly.
Of the mid-level resorts, the clear winner is the Wilderness Lodge. While it doesn't have rail access, you can take a quick walk or bus over to get Ferry access to Magic Kingdom from the Lodge Villas. The Lodge has a really nice Pacific Northwestern exterior and being newer (built in 94), quality designed and furnished rooms. I think the Wilderness Lodge has the best adult restaurant not located in a park or Deluxe resort in Artist's Point - I'd even argue that Artist's Point is better than most of the Deluxe restaurants as well. Coronado Springs has a neat Aztec feel to it and some fun tex-mex restaurants and an amazing water splash area, but the rooms are very campy and cheap looking. Caribbean Beach is similar and probably about equal to Coronado Springs with Port Orleans being just a small step down. All of Coronado, Caribbean, and Orleans are going to require you to bus to your park locations and that is going to add a lot of time each day - factor 45 minutes to an hour for travel time each way. The factor that keeps the mid-level resorts in the game is that they are cheaper for Disney standards and they are all relatively newer with fancier restaurant choices. I think Disney's done a good job of keeping each of these attractive even if they are obviously a step down from the Deluxe resort locations.
Skip These Choices
There are three nicer hotels near Epcot in the Boardwalk Inn, Yacht Club, and Beach Club. Generally what I'll say about all of them is that they are geared toward older families and adults rather than kids under ten. They also don't have very good access to any of the parks, including their neighbor Epcot (it's harder to get to Epcot from the Yacht Club than it is to get to Magic Kingdom from the Grand Floridian). I wouldn't be upset to stay in one of these three, but if I'm spending the same money I don't know why I wouldn't just stay at the Polynesian instead.
As for the lower tier hotels - Art of Animation, Pop Century, and each of the All-Stars, avoid them if you can at all afford it. The huge drawback for me was that rooms in these hotels do not have their own climate control. You are stuck with whatever the hotel puts the temperature setpoint. This can be okay at night when you can just keep adding blankets to the 68 degree air, but during the day the temp seems to get cranked up high and drives all residents out the door. For whatever reason, not having personalized HVAC control just bugs the crap out of me. Oh, also, the bus distances from these parks are pretty long - expect an hour to be your travel minimum.
Honestly, I have no data at all on the private hotels because they've never been affordable compared to the Disney-run facilities. I know there is the Swan and Dolphin, Buena Vista, and the Wyndham, and there are probably a few more on campus. I guess my take on the private hotels is that - if you're going to travel to Orlando to make Disney World an experience, why not make your hotel be a part of that? The customer service of Disney is very hard to beat in any of their hotels and you have the added bonus of random acts of Disney happening while you're there (run into a character, face painting, impromptu hula dance, singing with indigenous pacific northwest tribes, etc.). Plus, you can't get monorail or necessarily bus service from the private hotels... which means more than your fair share of time spent at the cramped and crowded TTC.