Welcome to planDisney Cara!
Lots of questions, so let's jump right in!
The best swimming pool at Walt Disney World (in my opinion) is
Stormalong Bay at Disney's Yacht and Beach Club. This pool has everything from a sand bottom, to a small lazy river, a waterslide, and all around fun! When my family is planning on a lot of pool time on vacation, we stay at Disney's Beach Club for sure. These 2 resorts (Yacht and Beach) share this amazing pool area and are within walking distance to
EPCOT.
The closest resorts to the Magic Kingdom are Disney's Contemporary Resort and Disney's Grand Floridian Resort and Spa. Both of these resorts have walkways so you are just a 10-15 minute stroll away from walking down Main Street U.S.A. Boat and monorail service are also available to the Magic Kingdom from these resorts. Disney's Polynesian Village Resort is also walkable to the Magic Kingdom, but it would be the longest walk of the 3.
To get to Disney's Animal Kingdom, you will need to take a bus if using Disney Transportation. The closest resort is Disney's Animal Kingdom Lodge.
Disney's Hollywood Studios is walkable (about 20-30 minutes) from the resorts on the Boardwalk (Boardwalk Inn, Boardwalk Villas, and Yacht and Beach Club). If you stay at Disney's Caribbean Beach Resort, you can hop on the
Disney Skyliner for a direct route to Hollywood Studios.
Disney Springs is can be accessed by bus from any of the Disney Resorts, and by boat taxi from Disney's Port Orleans Resorts.
So that is an overview, but there are many, many other ways to reach these Disney destinations.
Disney transportation makes zooming around property super easy, so select your resort then you can figure out the best mode of transportation to get where you need to be. Have fun finding that perfect resort!
Cathy