But the weather is hit or miss. December, January and Feb in particular might be cold enough that swimming is only for the really brave. Then again, it might be 80.
October has gotten much busier - and has moved seasons. September is still very quiet. Hot, however - still hot in September. And rainy.
For a budget trip, look to go during value season. However, its only going to give you a break on hotel rooms. Pretty much all other costs are constant - food isn't cheaper, park tickets aren't cheaper (although sometimes they run promotional packages for the fall). The break on hotel rooms can be gotten year round staying off site.
Another thing you should know as a first timer - in the "off" season, park hours are shorter and some attractions (the less popular ones) close down. To make up for the big crowds durng busy season, parks are open late and there is often a lot more entertainment going on. So in September, Magic Kingdom may close at 6:00 every night and you may never have an opportunity to see Spectromagic - where it is more likely to be open until 10:00 or maybe even midnight over the summer with Spectro running twice a night.