Kelly,
ANY time you are in Disney is a good time!
I would try to come in June if at all possible, and the earlier in the month the better. This will help you as far as crowds and heat both. That said, I have traveled in June before and was very concerned about it, and was pleasantly surprised. It was neither as hot nor as crowded as I had feared, and we had a great vacation.
Because this is your first trip, I recommend that you consider a service like
www.tourguidemike.com. This website will allow you to purchase a customized touring plan that suits your families' needs, and allows you to see and do all that you want to take in on your trip. I've not found this to be necessary in the off-season, but for peak visitation periods and very brief vacations it can be an excellent tool.
No matter which month you come in, I'd recommend investing in some handheld battery powered fans (I bought mine at a chain store for about $1). They are wonderful!
Hakuna Matata ~ you will have a great vacation no matter what time of year!