Hi Aaron!
Your question cut off before you gave ages for your children, but never fear, an easy answer is here! First off, the September time frame is my very favorite! Warm enough to feel like summer, but not so hot that you melt. The crowd size is ideal, as lines are shorter than during peak times, but the parks still are buzzing with a fun atmosphere.
As for the resorts, here are two recommendations. With smaller kids, I recommend for your first visit that you stay either on a monorail resort (
Grand Floridian,
Polynesian, or
Contemporary) or the
Wilderness Lodge. Of the four, select the one that has the theme that you think would be the most fun for your kids.
If you have older kids (tweens or teens), I think that the Beach Club or Yacht Club are the best. Just make sure that you get park hopper tickets so that you can go into Epcot's World Showcase every night, regardless of whatever park you visited earlier in the day.