Your first rifle shouldn't cost a shitload, and trying to kill a gator at range is going to be pretty hard because they're usually in rough terrain, are very low to the ground, and are usually pretending to be a log. Shooting them close improves your stopping power and ability to hit the vital organs. If you're worried about them getting a last laugh in on your shinbones, I'd shoot them from up high, like a truck bed (park near water, sit in lawn chair in bed, drink beer, wait) or from a tree (spot, climb tree, shoot).
Blood is absolutely right, it is a bitch to calibrate a scope. If you don't know how (and given these questions it seems safe to assume you don't) you're going to throw your money away. Furthermore if you're used to a shotgun I'm willing to bet your aim is less than stellar and a lot of that scope's capacity is going to be wasted due to a lack of form. Get a solid old rifle and learn to use it before you invest in a fancy scoped manhood compensation device.
And I'm calling bullshit. 7.92x57 IS > 7.62x54R. I've got an M44 as well, so this is no idle comparison. I've held both rounds, and the IS doesn't neck down nearly as much as the 54R.
My only caution against buying a Mosin as that there's no saftey and the bolts tend to be rough. Hunting deer you would make noise locking the thing, since its not cool to carry around the woods a loaded and unsafetied gun.