Emotionally, what should donors be expecting?

A lot. Donating a kidney is a precious gift that the donor will be doing. If everything goes the right way the donor will be having a very gratifying feeling. Some surgeries may have some minor complications that create anxiety in the donor but they are usually short lived.
Which organ. If you are an individual donating organ for the benefit of another ones life, I commend you and may you be blessed. Most often in this scenario it is donating a kidney. Meed more info to elaborate .