Hi! I think the idea of splitting your stay to maximize the transportation convenience is a great choice. We often do the same thing, and it has worked very well for us. The Beach Club sounds like an excellent choice for your Epcot resort (kids love Stormalong Bay), and you are right about the convenience there. It's a very short walk to Epcot (like less than 5 minutes) or you can take a boat and you can either walk (approx. 20 minutes but a nice flat path) or take a boat to Disney-MGM Studios.
As far as the monorail resorts go, your choices would be the Contemporary, the Polynesian, or the Grand Floridian. The Wilderness Lodge is also a Magic Kingdom area resort, but you must travel to the Magic Kingdom by either boat or bus from the Wilderness Lodge. The only resort that has a walking path to the Magic Kingdom is the Contemporary. Riding on the monorail is a very fun, efficient way to travel to the theme parks, and I love riding it.

The way the resorts are layed out means that the first resort to drop guests off at the Magic Kingdom is the Grand Floridian, then the Polynesian, then the Contemporary. Then on the way back from the park the order is reversed (Contemporary gets dropped off first and so forth). It's not a long ride around the loop though, so which monorail resort isn't a huge deal maker or breaker.
I have found the All Star busses to be efficient, but the ride itself is longer to the parks then some of the other resorts. I think if you are looking to maximize your convenience I would stick with the Beach Club and one of the monorail resorts (I would just pick which one of those based on which theming you like the best). Your DS can always get a chance to ride the bus to the theme parks that aren't served by the monorail or boats at the resort you're at at the time.
Another good recommendation to save time is to pick up a copy of the Unofficial Guide to Walt Disney World by Bob Sehlinger. It has detailed descriptions of the attractions (and mentions which ones might be frightening to small children so there aren't any surprises) and offers excellent time saving touring plans of the various parks. If the parks are a little too "commando style" for your vacation style, then they also offer customized touring plans to help minimize your wait in line based on when you plan to arrive and depart the parks and building in any needed nap times.
Enjoy your first trip!
