My favorite varmit rifle!!! Depends on the varmits.
For gophers, I would pick my 513T Remington .22. For prairie dogs, most have been shot this year with the Browning .22 Hornet, the .222 has taken more prairie dogs for me than any other caliber. Lately, I have used the custom barreled .223 more for dogs. Also I have an old 700 in .22-250 that has probably killed more varmits than any rifle but my .222. The .22-250 is on its 3rd barrel. For woodchucks, my three favorites are .22 Hornet, .222, and the .22-250. But have shot them with everything from the .22lr to .300 Win. Don't get to hunt chucks much any more.
For coytes, the .22-250, .22-250 AI and .220 Swift are favorites for called dogs or shots where bullet blow up is important. For general coyote shooting, my favorites are my 25-06 with 100 grain bullets, and my windy day coyote rifle a semi target barreled .300 win. For me it is difficult to pick a favorite. I love 'em all.
The Hornet is a fun gun to keep in the pickup for informal close varmit shots.
For serious prairie dog shooting I would go with my .223 and a .22-250 for long shots.
For coyotes, I usually have a big .22 in the truck and either the .25-06 or .300.