Hello Debbie!
If you are wanting to stay at a Walt Disney World Resort hotel close to the action, then I would recommend one close to Magic Kingdom park or Epcot. With a 3-year-old, I would probably spend a lot of time at Magic Kingdom and would ultimately recommend
Disney's Contemporary Resort.
The ability to walk to Magic Kingdom or take a quick monorail ride back to Disney's Contemporary Resort is priceless. My children are so excited when they see the monorail go right through the resort! You can also ride the monorail (with a transfer) to Epcot. The transportation options, delicious restaurants, and splashtastic pools rank Disney's Contemporary Resort in our family's top 2 Walt Disney World Resort hotels.
I would also suggest
Disney's Beach Club Resort. Stormalong Bay, the resort's pool, is amazing. With a lazy river, kids' water slide, and sandy beaches, your 3-year-old will never want to leave the resort pool. Disney's Beach Club Resort is also within walking distance to Epcot and Disney's Hollywood Studios or you can opt for a fun boat ride to both theme parks.
Deciding between May and September is a tough choice. September will have hotter weather (it's really hot), less expensive resort rates, and lighter crowds. If you go later in September, you can also catch Halloween festivities like Mickey's Not-So-Scary Halloween Party, which is my favorite party at Walt Disney World. The beginning of May will include moderate weather, manageable crowds, and special events such as the Epcot International Flower & Garden Festival. If I was on a budget, September would be the winner.
If you have any other questions, please come back and see us real soon at the Disney Parks Moms Panel. Have a magical vacation!
Tania