None of these rounds are good for truly long-range shooting.
I'd just use .22LR and learn my drops. Spend the money on a rangefinder instead, and go to town. It's a learning experience well worth having. Remember: BP cartridge shooters use .45-70 rounds with about the same muzzle velocity as common .22LR for 1000-yard competition. You should be able to hit targets at 200+ with .22LR.
The .22WMR is more for doing the same thing as .22LR but with a lot more energy, for ethical small game hunting. E.g. it took several rounds of .22LR for my friend to kill a desert jackrabbit. Good .22WMR JHP would have killed it in one shot.
.17HMR can be a crazy accurate round at 100 yards. I've seen some amazing 10-round groups, but our club has a 100 yard indoor range without wind. Most .17HMR comes with fancy-schmancy varmint bullets, not target bullets, and you pay for them. You might as well get a .223 instead, and be good for a lot more distance, and of course, .223 has a wide variety of match bullets and factory match ammo available for it, as well as bulk ammo.