To avoid hot weather, hurricanes and crowds, I would look into early November or early December. September is hot and humid and it is hurricane season. It is also usually the time of free dining. Big crowds. October might be good if you don't go around Columbus Day or Halloween. Late September through October, they have Mickey's Not So Scary Halloween Party (
MNSSHP). Of course, that means the Magic Kingdom closes early and if you want to attend the party, you have a buy tickets. Beginning of November, you should catch the tail end of the Food & Wine Festival. It's included in your admission to Epcot. I've never been but lots of people rave about it. The only other time I've been when it is not crowded is the end of August right before free dining starts. It was hot, hot, hot. But since the crowds were so low, we were able to spend lots of time at the pool because we would get most of the major rides done very quickly.
I wouldn't, myself, spend less than 6 days there. Magic Kingdom and Epcot should have 2 days to totally explore the parks. Hollywood Studios and Animal Kingdom can be done in a day.
Like Ev said, the advantage to staying onsite is the convenience. You will not need a car for any reason. Disney will transport you from the airport to your hotel and back again at the end of your trip. All the hotels will print your boarding passes for you. If you have a late flight going home, they will hold your carryon luggage until it is time for you take the bus back to the airport. If you stay offsite, you have to worry if you catch your shuttle back to the hotel from the parks because there might not be another on. Disney buses will run 2 hours after the park closes. It's very easy when you stay onsite. No driving, no navigating the roads, no parking fees.
Ev talked about 2 of the hotels there. They are what Disney considers their Deluxe hotels. They are a couple of the more expensive hotel but very beautiful. They also have values, moderates, and DVC hotels. Values are your basic run of the mill hotel rooms (Holiday Inn) but with major Disney theming. They are the cheapest and if you are really only looking for a place to sleep, they are wonderful. The 4 value resorts are All-Star Movies, Sports, Music, and Pop Century. All-Star Music also offers Family Suites. Those are connecting rooms with a queen size bed in one room and a pull-out sofa and chair in the other room. I believe there are 2 bathrooms and a small kitchenette.
For the moderate resorts, they are slightly bigger rooms. Port Orleans Riverside offers rooms that have a trundle bed for children. But if you use to more space, that might not even work. Bopsmom can explain DVC resorts....I still have problems understanding all that.
It's very easy to make all the plans yourself. You won't get a better deal by using a
travel agent but the really good ones will spend their time looking for deals and promotions for you. It's just another one of the time and convenience deals. Some travel agents will make your dining plans for you others you have to do it yourself. If you have
AAA, they often run promotions for some good discounts. But if you go that route, you will have no control over your reservation. Everything will have to be done through your AAA agent. I've heard on here that there are some AAA agents that do not know alot about Disney including supplying false information. Not on purpose or anything but they just don't know. I've used
Dreams Unlimited and they were very easy to deal with.
You could do a package deal which will include your tickets. You could also book your room and buy your tickets separately. You can use AAA on your own to book a room discount. If you do everything separately, you can buy your ticket through
Undercover Tourist. They have the cheapest tickets and if you sign up with Mousesavers, they will send you emails with a link to save even more. Since this would be your first time, I would only buy base tickets. That will allow you to enter on park per day. You can leave that park and return to the same park later that day. You cannot hop between parks with those tickets.
You may also think about signing up for TourGuideMike. He has wonderful advice on how and when to tour the parks. Some of his information is outdated but his forums are filled with great people who know their stuff. I've used his advice to tour and have avoided lines like you wouldn't believe.