The upper end is limited more by how much recoil you can tolerate, an important consideration as you may be doing a lot of shooting. Preferred varmint calibers are usually somewhere in the .22 center-fire range, like the .223 or .22-250, but there’s all kinds of wildcat cartridges available, and the sport is particularly popular with hand-loaders.
Don’t worry if you only own one gun - a deer rifle, you’re breaking in a new deer or antelope gun or simply want to get used to it before the season. In that case you can go with a larger caliber but use reduced recoil loads or accelerator sabots. With the latter you can shoot .30-06 bullets down to 55 grains.
Small varmint hunting is not a particularly rigorous activity either. In fact, most good hunting areas are accessible by an off-road vehicle so you can load your ATV with guns, gear and some amenities like a cooler for lunch, chairs, even a shooting bench if you prefer.
For essential equipment you’ll want a bipod, tripod or other means of stabilizing your gun. Because it’s primarily long-range shooting, binoculars and a spotting scope are invaluable. And of course, you should wear the proper eye and ear protection.
The rest is simply locating your quarry and making a good shot. For the most part you’re in open terrain, fields and pastures. The amount of available cover and how close you are to your quarry will determine how much or how little camouflage you need. It may take patience so it’s best if you can set up in the shade and make yourself comfortable.
A few words of caution are also advisable. You may be around livestock so always be sure of your target and what’s beyond, and make sure there is some sort of solid backstop behind it should you miss, or your bullet pass through. Otherwise, practice all the standard firearms safety procedures and be considerate of landowners and other land users.
Groundhog Day may only come once a year on the calendar, but you can re-live it many days over in the middle of the summer. Not only does it offer some great recreation, you’ll be doing the landowner a big favor, which could work in your favor when it comes to gaining access for bigger game.