RE: Best Varmint Rifle and Caliber?
HEAD0001's points are good. I pick from a couple different ARs, a CZ550 Varmint in .22-250, and a CZ527 Varmint in .223.
ARs can be fun to hunt prairie dogs with, but I generally prefer the .22-250. It's so heavy though that if I'm going to do any kind of walking (like, coyote hunting), the ARs or 527 fit the bill much better. The 527 is built on a "micro" Mauser action, very strong, very reliable. I also like the set trigger. In spite of the heavy barrel, it's nearly equal to what you'd expect from a standard-weight deer rifle. A bit unusual looking in that its single stack, five-round magazine is readily visible (not flush).
Glass is a big consideration. You can get by with 4x, but you'll probably feel better with something more powerful. I'm using Burris FFIIs in 6.5-20 and 4.5-14. I prefer the 6.5-20 simply because it has the Ballistic Mil-Dot (and I'm used to estimating range with a Mil-Dot reticle). With the 6.5-20 on the CZ550, I probably have somewhere in the neighborhood of $950 invested. The CZ527 with the 4.5-14 comes in right around $800.
I'm loading .223s with 60 grain Hornady SPs, and the .22-250 with 50 grain Hornady V-Maxes. Though both my Colt and Rock River ARs like the heavier bullets, I loaded a batch of .223s with the lighterV-Maxes for the CZ527just to see how they shoot. Have towait until the prairie dogs un-hibernate to find out.