Using the picture below as reference. The 2 grey disks are waypoints on a path, the red disk is what will be moving. What do I need to use so that the disk will move from one disk to the other, and smoothly change its rotation over time to match where it is going to?
I need it so that entire movement does not necessarily happen in one frame. The time it takes to move between waypoints can vary .
First, let me answer the specific question you ask. In the absence of the your code all I can do is outline some pseudo-code.
transform.rotation = Quaternion.Slerp(disk1.rotation, disk2.rotation, precentageBetweenWaypoints);
That is the third parameter is the fraction of the way the disk is between the two waypoints.
Note depending on your goals here, there may be a better solution. You could use your waypoints to generate a spline. Then you can align the disk by using a point a bit forward on the spline from the current position of the object. iTween is a free way to generate the spline. You can use iTween.PointOnPath() or iTween.PutOnPath(). There has also been some spline code posted to UA.