Based on your statement about buying a deer barrel later, I'd go for the .357 Magum or a .223. Both offer cheap ammo and low recoil (although the .223 will be loud). Both "can" be used for small deer, but neither is ideal. The Maxi will cost a premium if you can find a barrel, the .45 will have to be the straight .45 Colt, not the .45/.410 barrel if you want accuracy. The .44 is not a bad choice, except that ammo will be relatively expensive - price some commercial .44 Special ammo, it isn't cheap. You can buy commercial reloads in most of these chamberings, if you can find them, to save costs. Save the deer barrel for later when you have more time to think about it. The first barrel should be for fun and learning.