We always went around Spring Break in March.. Not too hot and still comfortable weather.
We never stayed anywhere except the Polynesian which is on the monorail line. We LOVE that place. SO easy to jump on the monorail or boat taxi to MK and you are there withing minutes. If you need to run back to the hotel for naptime, etc, it is SO easy. It is not the cheapest place but it was always worth it to us.
As for arrangements, I always dealt directly with WDW. They send an informative DVD to you that pretty much details all the resorts, rides, parks, etc. Book early for character dinners, breakfast, etc. O'Hana at the Polynesian has a nice character breakfast. Chef Mickey at the Contempory has a good All American buffet with characters. There are several meals to choose from.
We got the passes that were good from the time we checked in until midnight on the day we checked out. Any park, any time, as many times as you wanted. Also, 1 park opens early daily for guests on the monorail line. There are other perks as well... we did a private safari that was awesome at Animal Kingdom.
It is a straight shot from DFW, easy peasy! We always took a cab and were at the hotel within an hour... about $100. Yes, there is a free shuttle but you never know how crowded it will be and how long it will actually take you to get to your hotel. It was not worth it. You don't need a car.
Enjoy and take it all in. You can't see it all at once.. choose parks which are more related to your children's interest.