Good morning to you Brian.
If using an exterior door keep in mind that these are sealed tight all around so therefore you'll need to have an access for the air-conditioner return air for the room, which is typically the space between the floor and the bottom of the door in most interior door applications. I'm thinking most new homes are vented rather than using the interior door for the return air.
We have double exterior vinyl over solid wood french doors leading into our room and they do a very good job with keeping the sound contained.
As Jake suggest, I believe the interior walls will be more of an issue than the door leading into the room.
