Your shooting distances, style of hunting, and what you consider to be a varmint will all go into consideration on what caliber and optics you get. I see guys show up to go hunt predator at night with a 22-250 26" heavy barrel and a 6-24 x 50 turret scope. Great rig for the P-dog towns, static ground hog shooting and off the bench, but too darn busy for the coyote hunt.
A great rig for yotes out to 300 would be a 223 with a light weight barrel, 3-9 x 40 scope with a hold over styl reticle and a propper bullet to take the dogs down. generally speaking, target and hunting dont mix when trying to build a gun to fit both areas.