The .22-250 is hard to beat...therefore its' reputation as "the varmint caliber". It offers the flatest trajectory, excellent accuracy, several bullet weights/choices and several good manufacturers.
I'm very partial to the Savage/Stevens line of rifles, due to their out-of-the-box accuracy.
Often the caliber choice can be determined by your location. Bullets skips and ricochets can be a varmint hunter's nightmare with residential housing as a background. If this isn't a concern, then there's even more options in calibers.
I use a RRA A4 Varmint .223 for groundhogs, but I use a Stevens .25-06 for coyotes.
Good luck with your choices!
Good hunting, Bowhunter57