.17HMR is a .22mag necked down to .17. Ballistics? 17gr. bullet at 2500FPS? Somebody will correct me. Its a rimfire, not reloadable.
.17Mach 2 is a .22LR necked down to .17. Much weaker. Ballistics? I dunno, maybe 17gr. bullet at 2100fps? Also a rimfire, not reloadable.
.17 Rem is a centerfire cartridge. Pretty big. It shoots a .25gr. bullet at 4,000fps or so? Reloadable. Big difference.
The Mach 2 is not a 200 yard cartridge. _Maybe_ 100 yards. The HMR might stretch to 200yrds, usable. The .17Rem is a 200-300 yard cartridge.
If you don't want to reload, I'd recommend the HMR. If you want to shoot mice or rats under 100 yards, the Mach 2 would be OK. The .17Rem for serious varmit hunting.
I shoot a wildcat--a .357mag pistol brass necked down to .17. Shoots a 25gr. bullet about 3200fps. Love it. Light recoil, and does a good job disassembling small varmits.