I have experience with several varmint calibers and I think it comes down to what you plan on hunting and where. Coyotes at 50 yards in the brush require a little different mindset on rifles than ground hogs in open country.
A heavy varmint rifle in 22-250, 6mm, or .25 caliber is great for open fields, but seems a little clumsy in the brush. Been there, done that. It's fine if you rarely get into that situation but not the "best".
50 yard coyotes are perfect for .25-20 and .25-35 lever actions, yet most people do not concider them "varmint rifles" in a classic sense.
OK with that said, Single shot rifles like the TC Encore and Contender as well as the AR style rifles have one advantage over most of the other style rifles. It is very easy to change caliber and/or barrel contour while keeping the same trigger pull and basics of the rifle. (Where the safety is, or does it have a hammer to pull back?) Little things sometimes mean alot.
If you want a bolt action varminter I would suggest a moderately heavy barrel rather than a bull barrel, unless you plan to get into competition.
A mauser type action with a 20 inch bull barrel and beaver tail stock with a bipod is one heavy chunk of gun to haul around, seriously don't get this for your first rifle.
As far as cartridges go Most of the ones the guys have listed are pretty darn good I like the 6mm Rem for a heavy varminter and the .204 Ruger for general varmint work. The .204 Ruger has a lot going for it and may be the best fox round ever.
For a fast handling coyote rifle I have a .223 AR one upper light and the other heavy.
What ever you decide, good hunting!
Regards
Gene