I went last year to do this and lucked out. I was able to see all the fall/Halloween decorations during the first two days of my visit and then all of a sudden I walked into MK the next day and it was Christmas. Best of both worlds. I'll have to look up the exact dates of my trip.
As for low budget, that all depends on what type of accommodations you are looking for. If you want to stay on property the lowest you'll get is set up a tent over at FWC. A tent site there is around $75 a night and you can have up to 10 people per site. It is a great time of year to camp, not too cold at night or hot during the day. Plus, a lot of campers go all out in decorating their sites and it's a lot of fun to see their displays. If camping isn't for you then the budget All Star's are the way to go. If you don't mind off-site and go at the end of November and beginning of December you can find hotels for $30-50 a night all over Kissimmee.
As for must do's, there are so many. They had a great Christmas tree display set up at Disney Spring's last year. Each tree was decorated pertaining to a movie or character. It was also free to walk through. I enjoy just seeing the parks and hotels decorated for the Holidays.
Have fun!