Minimum of one week, two weeks would be great. More time allows for a slower pace. There's a lot to see on the property outside of the theme parks too, especially if you've never been here before. You'll want to visit the other resorts to take it all in.
Basically, the best times to visit would be when school is in session, no holidays. Our favorite times are the weeks between Thanksgiving and Christmas (but you do NOT want to be there for either - crowds are shoulder to shoulder) or mid January to mid February. The weather is great, the crowds generally low and few if any bothersome bugs. The Thanksgiving to Christmas period ads the wow factor in the form of their over the top Christmas decorations and festivities.
You can get to anywhere on the Disney property, any of the theme parks, any of the resorts, even their shopping, dining and entertainment district, Downtown Disney, from anywhere else on the property. From the campground there is a bus stop at every camping loop that will take you to one of two general transportation areas where you can hop on a bus (or a boat) to your desired destination. Your only limitation would be anywhere outside of Disney. For that you'll need your own transportation, or you can call a cab.
Jay & Peggy Monroe with Dolly
Can't take it with you - don't plan on leaving any behind
2016 Newmar London Aire 4553, Spartan chassis
Wrangler Unlimited toad