Hi, Jane!
Wow!
Traveling with 3-year-old twins will so much fun, Jane! You are all about to have a blast!
For accommodations, these resorts fall into two different categories, both Value and Moderate. Both are lovely, but each has its own unique features.
Disney's Pop Century Resort will be the easiest on your budget, as it is a Value Resort. It's closer to DIsney's Animal Kingdom Theme Park, Disney's Hollywood Studios and Epcot than Magic Kingdom. Transportation to MK will take a bit longer from this resort, simply because you're further away.
Disney's Caribbean Beach Resort features a fantastic shipwreck water play area near the pool and Pirate Rooms are available. This resort is closest to Epcot. Request a room near the main lobby and pool because this is one of the larger resorts.
Disney's Coronado Springs Resort, which is a bit closer to Disney's Hollywood Studios and Epcot, is a stunning resort with a fantastic pool (kiddie pool, too!) and great dining options as well. This is a very large resort, too, however, so if you decide to stay here, request a room near the main lobby and pool, perhaps Cabanas Village.
All of these resorts offer complimentary Resort Buses to the various WDW parks and Downtown Disney.
If princesses are more your style and you'd like a 2nd mode of transportation, try Royal Guest Rooms at
Disney's Port Orleans Resort-Riverside, which includes boat service to Downtown Disney as well.
Send more questions as you choose your resort, Jane; we love to help!