Since this will be your first family trip off-site, I would suggest you choose either Windsor Hills or Bonnet Creek. They are both very popular places to stay and recommended on this board. Here is a link to describe the differences between the two:
http://www.disboards.com/showthread.php?t=2629717&highlight=windsor+hills+bonnet+creek
If you think you would like Bonnet Creek, check out the we love Bonnet Creek thread on this forum. Most people book through ebay or Ken Price at
Ken@vacationupgrades.com.
If you want a private pool, then you will have to go with a 3 BR townhouse or 4 BR pool home at Windsor Hills. The 3 BR townhouse has a small splash pool, while most of the 4 BR homes have a larger pool with attached spa/hot tub. We usually stay in a 4 BR pool home in Windsor Hills.
If staying at Windsor Hills, you can rent through All Star Vacation Homes or Florida Sun Vacation Homes (we use Florida Sun). You can also book directly with an owner by going through vrbo.com or homeaway.com.
If you want to go the pool home route, there are communities near Windsor Hills that tend to be cheaper. This thread has good information about pool home neighborhoods near Disney:
http://www.disboards.com/showthread.php?t=2623627
Regarding rental car rates, check
www.mousesavers.com. They always have codes listed for the different rental car companies. Also, the transportation forum on this board in wonderful. Usually, there will be a thread about December car rental rates. Subscribe to that thread and keep watching rates. I ended up re-booking our minivan less than a week before our Spring Break trip after finding a code posted on the March thread. Book something now (to have as a back-up), and then keep following rates until you find something cheaper.
Good luck with whatever accomodations you choose. You will have a wonderful time offsite as long as you do your research and determine what would be the best fit for your family.