A high tooth count carbide blade 7 -1/4, will take care it. I like makita the best now, desalt also makes some very nice saws. Milwaukee some times the grips are just not ergonomic IMO. Any good quality saw will be good and not the cheapest.
I agree as previously posted that the porter cable saws were the best. I have several and they have been worked and are going strong. On the cheap side of saws I think makita comes in the best of the cheapies, and also the best with all the bells and whistles on the top end.
Just remember never let any part of your body be in line with the blade in case it kicks back. Also scribe the door with a sheet rock knife prior to your cut which will help with cutting as it will be better than a pancil or chalk line, and leave a nice clean edge. Remember to not mar or ding your the surface of your door when handling it and placing it on the horses, especially if it is a solid door, because they can be heavy and can make a mark under their own weight. If it is a hollow door make sure there is enough meat left that you don’t cut into the hollow core. Just some things off the top of my head. Good luck.