Hi Candice!
Congratulations on making the decision to begin planning your First Family Vacation to Walt Disney World!
Both Mid-May and September are great, non-peak times to visit Walt Disney World.
Personally, I lean towards September as the crowd levels are significantly lower than most other times of the year since not as many families travel right after their children begin school for the year.
In May, the weather is slightly cooler on average and a little less humid than September. In the first half of May, crowd levels tend to be a little higher with the popular Epcot Flower and Garden Festival taking place. You'll also find periodic Cheerleading Championships and Grad Days/Nights taking place in May that can affect crowds in certain parks on certain days. Crowd levels on a scale of 1-10 tend to range in the 6-7 area throughout the middle part of May.
In September, beginning mid-month,
Mickey's Not-So-Scary Halloween Party begins taking place on select evenings. This is a specially ticketed event that your little ones may really enjoy as an added-bonus to your vacation. Crowd levels mid-late September range in the 1-3 level, which for me, makes it well worth putting up the the slightly elevated humidity.
I hope to hear from you again Candice if you have more planning questions!
Wishing you a Magical time as you begin to make your plans for an amazing, family vacation.
Kirsten