Varmint rifles typically are small bore, high power and extra high velocity flat trajectory cartridges rifles, able to take down small til medium game from rat till even feral dog. Equipped with high magnification telescopic fights for long range shooting, experienced varmint hunters have good results at target even at extreme far away ranges.
As so called varmints are in general smaller pest animals, there are not any need for large and heavy projectiles. In our case, light and fast bullet which give laser-straight trajectory and make possibility take quick aim and accurate shoot so bullet velocity for today varmint rounds usually in exceed 3,000 ft/s (910 m/s) and even more. Fast bullet allows extra long range shots with a really short time of projectile flight, and little or almost no change in trajectory at long ranges. Make your range finding measurements rough and actually a bullet drop of only a couple of inches is enough to make miss at small and far way target like groundhog or crow sitting on rock couple of hundred yards away.
Also such type of fast and lightweight bullets tend to fast disintegrate or even explode in target on high speeds, so avoiding possible ricochets and make quick and humane game animal take down. Another good reason for the rifles with small calibers is their light recoil which is far more comfortable then heavy hitting .308 or something even larger.
Heavy match type rifle barrels are common on such setups, targets are not intended to be dragged at home and put on table as tasty dinner (crow soup anyone?), so more shots can be fired at them and heavier barrel in such case give end user more time till overheating occurs and rifle accuracy going down. To even more expand varmint rifle possibilities, steady and very stable rifle rests or shooting benches are often used at varmint hunting.
Two of most popular varmint rifles calibers, which all firearms manufacturers which have varmint rifles lines produce on numbers, are no doubt 223 Remington and 22-250. As both of them has wide rage of factory made high velocity lightweight bullets in the weight +/- 50 grains, together with good choice of reloading supplies, this made 223 and 22-250 one of this must have choices for any varmint shooter, beginner or not.
Scope for typical varmint rifle is high magnification variable telescopic sight with thin range finding reticule for aiming and shooting at distant targets. Popular choice of reticules for such type scopes are classic Mil-Dot, Zeiss made Rapid-Z Varmint Reticule, Leupold Varmint Hunter Reticule, Schmidt & Bender Varmint Reticule and other popular choices, sometimes even with reticule illumination feature.
Popular choice for varmint rifle action is single bolt action rifle, of course there are also semi-auto setups, but often they require more resources to put in to achieve accuracy required for long range varmint shots. In urban areas for safe shots at average city pests like rats, some varmint hunters successfully use all available line of air guns, from precharged PCP guns, till break action spring loaded to avoid misfire from high powered bullets.