My warmest welcome to
planDisney, Brian. Walt Disney would have gleefully approved of your train transport choice. Indeed, he loved trains so much that he built his own hobby railroad in Holmby Hills, called the Carolwood Pacific Railroad, with 2615 feet of track.
Guests traveling to Walt Disney World Resort by Amtrak trains may arrive at either Kissimmee Station, Orlando Station, or Sanford Station. From all of the locations, you may take a taxi/Uber/Lyft, as the Minnie Van Service does not travel to these locations. As you mentioned a preference for Kissimmee Station, the expected taxi ride time is about 30 minutes.
The Orlando and Sanford Stations have car rentals available onsite. The Kissimmee Station has car rentals available near the station, and I know some companies will pick up customers with rental reservations. From the Orlando and Kissimmee Stations, you can access public bus transportation via LYNX. This cost-effective choice is likely to add significant additional time to your journey.
Disney's Animal Kingdom Lodge is truly a zen oasis. We recently had breakfast at
Boma - Flavors of Africa - such delicious food on offer! I highly recommend it if you can fit it into your magical Walt Disney World schedule. Brian, if you need more train fun, listen out for the call of the whistle as you travel aboard the
Walt Disney World Railroad. Enjoy making those unforgettable memories, Louise.