Winter next year. Without sounding blasé I'm not too concerned about cost at this stage.
If money is no object and transportation to the theme parks is paramount, then there are 6 options to consider: the 3 Monorail Resorts (Grand Floridian, Contemporary, & Polynesian) and the 3 Epcot Resorts (Beach Club, Yacht Club, & Boardwalk Inn).
All 6 have extensive activities for families. All 6 offer better transportation.
In general, the buses should be avoided as much as possible. Yes, lots think the buses are fine but compared to other modes of transportation, they are pretty much at the bottom. Buses stink when leaving the Magic Kingdom after the Wishes fireworks show.
If you intend to spend most of your time at MK, then go with a Monorail Resort. If you intend to spend most of your time at Epcot and DHS, then go with an Epcot Resort.
If it's a matter of wanting to spend a lot of time at the resort, I'd go with either Yacht & Beach Club (which share WDW's best resort pool and is close to the Boardwalk) or Animal Kingdom Lodge (AKL).
As a stand-alone resort, AKL is excellent, perhaps WDW's most exotic and arguably its best resort. However, it's also the farthest from most of the parks.
Grand Floridian has the largest rooms, Wilderness Lodge and AKL the smallest of the Deluxe Resorts. You can get a larger DVC Studio room at AKL but this is in Kidani Village and is away from the main AKL building, which is where all the excitement is.
Which is the "best" is mostly a matter of taste. It really depends on which theming appeals the most to you.
My experience is that plenty argue over which is "best" but, ultimately, it comes down to which theming they like the most. The reasons why "their resort" is the best often are justifications after-the-fact. In my opinion, if you look at the resorts objectively, there is no best. It's simply a matter of your priorities.
Again, if transportation is most important, focus on the 6 resorts I mentioned. (I've stayed at them all and don't really have a favorite.)
