Hello Scott and thanks for bringing this great question to the Disney Parks Moms Panel!
A FIRST trip is indeed a magical experience. You have already done some of the hard work of identifying what is most important to you: ease of transportation and great pool. Given those priorities, the resort hotel I would choose is
Disney's Polynesian Village Resort.
This South Pacific themed paradise will have a newly renovated central pool area, ready for your enjoyment next summer. Along with the great pool, there are many
recreation options such as boat rentals, fishing, and campfires. You will be able to view Wishes, the Magic Kingdom's firework spectacular, from the beautiful white sand beaches of the resort. If you obtain a theme-park view room, you may even be able to watch them from your room.
Access to both the Magic Kingdom and Epcot is just a whoosh of the monorail away. And, complimentary bus transportation is available to Disney's Animal Kingdom and Disney's Hollywood Studios. Two other resorts, Disney's Grand Floridian Resort and Spa and Disney's Contemporary Resort, share the monorail line, adding a large number of great dining choices within easy reach.
I hope this helps you with your decision. No matter which resort hotel you choose, I am sure your trip will be filled with pixie-dust!
See ya real soon!
Anne