The Swan is my preference. It has two sinks, and despite the slightly smaller rooms, has queen beds (Dolphin has double). It was just totally renovated. Dolphin not yet.
Price, depends, but usually Swan tends to be a few dollars more. I always have used Starpoints so don't pay.
They do offer a deal with guaranteed connecting rooms (something Disney resorts do not offer). Call and ask.
They provide small coffee makers and coffee. If you need more, like any hotel, find a maid cart and ask!
Garden Grocer is banned from delivering to the Swan and Dolphin. You can buy milk at the resort I believe but also the Screen Door General Store at the Boardwalk is a short walk, as is the Hess gas station.
I've never used any activities, but they do seem to offer some sort of day care for folks dining in the evening. I think that you can contact outside agencies for nannies. Never used.
Hope this helps!