My thoughts, cut the hickory and run with it provided its straight and rather clean. I have all 3 in the rafters but usually look past maple and elm to use hickory.
In general soft maple will be silver or red maple, hard maple will be sugar(most here call it rock maple I think), even Norway maples. A good field guide will help or you could find the info on line, but in general the leaf shape will be an easy way to tell the difference. Hard maple seems to be a very snappy wood but I have had it fail under tension around the slightest problems with the grain.
Elm...2 general types, red and white. I can split red elm by hand but white has interlocking grain to the point I will always use a saw and cut out staves. Its my understanding from reading that most prefer white and dont consider red much of a bow wood but some of my better elm has been red but always have had some user error when working with it lol. The white elm I have harvested is a bit light. I have a white elm bow that I did everything but put a finish on thats been sitting by my computer here for a year. Its average I suppose but started other projects after shooting it in. However I got an elm bow in the bow trade a few years ago thats outstanding, I'll put a pic below. I think that wood was harvested in northern Canada.
IMG_3227 by
Mike Allridge, on Flickr
If you have a rack full of bows try maple or elm. I'd like nothing more than to make a good elm or maple bow from wood I harvested and It can be or has been done. I like when people post white wood bows here. Just use good dimensions for the material you have. You may also have black locust, another excellent bow wood or even osage grows in the southern part of the state I hear. However if you dont have many bows under your belt hickory I think its the best bet because its more consistent material from the 3 you mentioned. Hope that helps you out some.
Mike
