BigJake-- I've only been shooting the .17 Rem caliber rifles for about 20 years, but I sure am glad I started shooting them back then. I have used the .17 Remington for prairie dogs, gophers, various non-mirgratory birds, as well as fox, badgers, AND coyotes!
The bullets I have been using for prairie dogs are the 20 gr. V-Max (when the wind isn't whipping too fast), the 25 gr. Hornady hollowpoint, the new 25 gr. Hornady V-Max, 25 gr. Starke, 26 gr. Genco, and the 30 gr. Starke. I use the bullets below the 30 grainers strictly for varmints and use the 30 gr. Starke for coyotes and once in awhile I use them on varmints.
I have shot some of the 30 gr. Berger LTBs, 30 gr. Kindler Golds, and 30.8 gr. Hammetts at paper, but haven't taken any of them after live game yet. I just purchased some of the C.E. Nagel 25 gr. bullets (he has the dies that Clint Starke used to make the fine Starke Red Prairie Varmint bullets) and he gave me about 20 of his version of the 30 gr. bullets to try too. I will also be tesing the 27.5 gr. Hammett bullets this spring.
The 30 gr. Starke bullet has been a fine coyote bullet for me over the years. I have taken coyotes with that bullet out to about 385 yards. However, I don't recommend taking many shots with the .17 Remington at that distance. I usually try to limit my shots to around the 250 yard range. I call coyotes, so unless one hangs up way out there, most of my shots are at 100 yards or so.
Like several of the other posters have mentioned, you need to be very careful where you place your shots with this small caliber rifle. Personally, I have switched to the .204 Ruger as my coyote rifle now and the. 17 Remington rifles I have will be mostly for varmints, like prairie dogs and gophers.
If you reload, it will be a GREAT varmint rifle for you. If you have to shoot factory fodder, then whether the .17 Rem is good for you will depend on how well it digests that factory ammo.
Regardless of what ammo you shoot, you'll find that the lack of recoil is a great selling point for this caliber. One can see hits on varmints through the scope. When people ask me how much recoil the .17 Rem has, I tell them that I wouldn't be afraid to place the butt pad up to the bridge of my nose and shoot it. Not sure I'd do that, but there is little recoil.
Good luck on your decision.