It really comes down to a few things.
What type of hunting and types of shots do you typically see? A 45-70 or 444 is going to carry more energy farther downrange than a 44mag and have a better trajectory for doing so. However, a nice lightweight lever action might be just the ticket for hunting the hills and super thick areas of SE Ohio.
Do you reload? Ammo availability as discussed above is quite variable between the rounds.
Budget?
What type of gun calls to you? I personally love the looks of my Marlin and prefer it over the looks of the Ruger 77/44 bolt action but the historical cool factor of a rolling block 45-70 is neat also.
Is this only for you? Because I chose 44 mag because I have a pistol in the same caliber and because I can load it with 44 specials and it will be the first gun my son carries deer hunting (more than likely). It doesn't have much in the way of recoil. My friend's Marlin in 45-70 while not a hard recoiling gun is definitely harder than the 44. I haven't shot a 444 so I don't know where it falls. Also the weight of the gun will have some factor in this as well.
All of them will get the job done, just how do you want to do the job?