I personally own a beagle and he's been a great companion as well as a hard worker out in the woods. They do have the best noses in the dog world ya know. I don't have any personal experience with the GSP's, but I don't know they might be good as well, after all it is a hunting breed as well. I don't know if there are any particular problems with beagles as so far mine has been healthy.
There's actually a great video about them which explains how healthy they are here :
beagles 101 and And although this is not exactly an article about hunting, it has lots of
info about beagles here
The smaller breeds don't have problems with any of their legs as well as they do not require extra calcium, so if you're not much of a breeder or dog lover, the Beagles are wonderful hard working dogs, that can easily go for 30-40 miles a day without a problem, with the proper conditioning of course.
I actually watched a show about trappers in the North and one of them had 3 beagles all of which were great. Oh and by the way, the Beagles have a distinct howl which separates them from the other breeds and they always make the sound when they're chasing game.