Who knows?
This subject was discussed a few threads ago, and you could search for FedEx and get some more detailed info, but I have tried to do searches before and they really don't narrow the choices down too much so I will try to summarize at least my impressions.
I have flown with people here with just about every imaginable background and experience. I don't think that there is a preferred background, although the system chief pilot has said in emails that the best chance to get an interview lately is to come from 121 regionals or internal (professional instructor, corporate department, box throwers). He also said only furloughees from USAirways need are being considered (as opposed to other carrier's furloughees).
As FBJ so eloquently put it, the most important factor is a recommendation from someone you have flown with that currently works at FedEx. That is critical. Any recommendation from an insider is good, but if you have flown with somebody that is much better, in my opinion.
The most prevalent background is former military (all branches), but that is probably a function of the large number of military trained pilots compared to civilian AND the built in good old boy network that goes along with being in the military. Its probably easier to find someone you have flown with if you were in the military than if you come up through the commuter/regional or corporate ranks, and thus easier to get a recommendation.
I get the impression you are considering FedEx down the road and trying to decide which path to take to give you the best shot at an interview. I don't think there is one best way, just get the mins as quickly as you can, network with everybody you fly with, and keep in touch with those you know who get hired on. Apply as soon as you meet the mins and then try to progress as far as you can where you are working until the call from Memphis comes in.
Good luck.
FJ