Re: 17hmr & fireball
17 HMR is rimfire. Cost is $12-16 per 50 shots.
17FB is centerfire. Only 2 kinds of factory ammo available and you're looking at $25 or so for 20 shells, which can be hard to find, BUT it's reloadable. The 17FB is basically the commercialized 17 Mach IV wildcat, which has been around for decades.
I would NOT use a 17HMR on a coyote unless it was within 50 yards and I had a steady rest on a still, broadside target. I would stretch the 17FB to 200 on a broadside coyote, though I still believe with most ammo, the 17FB is marginal for coyotes. Now step that up with hand loaded ammo with premium bullets and you've got a consistent fur cartridge.
The 17FB has a LOT more power than the 17HMR. Max range on fox would be about 100 yards for a 17HMR. A 17FB will easily stretch to 300 yards.