I'd not assume that a .44 Mag will be cheaper to shoot than a .308 or .30-06 for practice...one can find decent practice FMJ military ammo (non corrosive, reloadable) for the latter calibers for $3.50/box of 20.
Using some of that ammo in a Win Model 70 in .30-06, we managed 1" groups at 100 meters.

I'd go with the Encore in .308...better to have the 250 yard range without worrying about holding low/high and not need it than to worry about the .44's rainbow trajectory past 150 yards.