Well, I have been about 20 times, and only once we went 12/26 until 1/2. Thankfully, we had been so many times before on this trip. We were staying at AKL in a concierge room, so we would go to a park for about 2 hours or so, maybe 3, then back to the hotel and swim and relax, enjoying the resort.
The crowds that time of the year at the parks are unimaginable - crazy crazy busy. I was so glad it wasn't our first time to Disney, and there was really nothing we HAD to do. Of course the kids wanted to do Buzz Lightyear and stuff, so we'd head out, do that, then get out of Dodge.
New Years Eve at Epcot, by the early afternoon, it was literally wall to wall people. We had a cruise on Breathless booked for illuminations. That was fun, brought champagne (had dinner earlier at Flying Fish, worst meal I've ever had at Disney) and enjoyed illuminations while folks above us on the bridge at Epcot were very crowded together. Then we took a cab from Yacht club resort back to AKL - best decision ever.
I would say, if this is your first time, I'd either pick another time of the year (any other time of the year) or... Do lots of planning now! Go early to the parks and leave when it starts to get crowded! Get your fastpasses EARLY! Soarin was out of them within a couple of hours every day. So get the fastpass, then go relax, then use it later. If you miss the time on it, they usually let you use it later in the day, just not before the time stated.
Where are you staying? This can make an impact on your trip, as it's so busy that time of the year. I'd bring your own stroller.
I don't want to put a damper on this, but if it's your first visit, is there ANY other time of the year you can go? I've been several times over spring break, and it's nothing like the last week of the year/new years.
If you want to chat or need any advice, feel free to PM me. I love Disney!