Hi Andrew and welcome to the forums.
May I ask, did your relative survive the war? If he did, it might be very hard to find his papers. If he was KIA, there is a possiblilty to request his Individual Deceased Person File (293 file) which includes all the inofmration of his "autopsy" and burial and often has additional information as well. I just got one from a Lt. which has an eyewitness account of how he died. Others also have other official documents regarding his military service.
There are people who can help out when it comes to APO numbers.... go to thi spage (be patient, it is SLOW to load)
http://genforum.genealogy.com/wwii/all.html and scroll down to the thread APO ADDRESS. You might want to contact one of th epeople there as he seems to have records on all APO addresses.
Success!
Two good sites with tips to research are;
http://members.aol.com/dadswar/index.htm#frststep
http://www.forvalor.com/ResearchFAQ.htm