RE: .17 hmr
On paper a .17 HRM will shoot 300 yards.
I have shot factory scoped guns that would group the size of a dime at 300 yards.
The parrallax throws the bullets a little to the right, but if you know how to hold over for it - or you have it sighted in at 300 yards that is not a problem.
The 17 grain bullets are more accurate and the best accuracy that I found with the one that I shot was with the Hornady ammo.
Anything over 200 yards with the 17 will only cause a coyote discomfort and not much more because them little bullets are like shooting them with a pellet gun.
A 22 / 250 is ok for for predators, but I would buy a 220 Swift if you want bragging rights.
That is one fast cartridge.