For physical preparation, as far as I know just staying in good condition is the best preparation. Some folks have suggested that some strengthening of the abs beforehand might help in recovery. Smokers should stop entirely previous to surgery, to have the lungs as clear and clean as possible. In the immediate preparation for surgery each hospital/surgeon has their own requirements regarding fasting, laxatives, etc.
Spiritual preparation can involve getting back in touch with one's sources of spiritual strength and guidance. Some donors have found it helpful to request prayer support from their faith community (personal or anonymously).
I had the open surgery rather than the laparoscopic donation surgery as my surgeon considered it slightly safer for the donor (this was 12 years ago, when lap surgery was still not as common as it is now) and from all that I have read so far I would still opt for the open surgery if I had to do it again. In talking to the doctors about your options, I suggest you always put your greater safety above other considerations of faster recovery, smaller scars, etc. (or even the hospital's desire to make use of its expensive laparoscopic equipment.) Keep in mind also that complications from laparoscopic surgery vary widely according to how many surgeries the doctor has done previously, as there is a sharp "learning curve" even among well-trained surgeons.
best wishes,
Fr. pat