Coyote or groundhogs at close range, any rimfire. At extended ranges any 22 centerfire, but I think 223/5.56 is the most versatile. If legal where you live a 22 center is just fine for deer size game out to about 200 yards if proper ammo is used. If not legal then you have to move up, but the last time I checked the regs there were only 4 states that did not allow 22 centerfire for deer that also allowed any other centerfire rifle cartridges. There are a handful of other states that are shotgun, muzzle loader only, and a few more that allow a limited selection of mostly handgun cartridges in rifles.
A 243 is enough gun for any deer that ever walked and is borderline acceptable even for elk size game. That sounds like the most likely choice for you. You can go up to something in 26, 27, 28, or even 30 caliber. They would be better options for game larger than deer, but don't kill a deer any deader than a 243. They would be less desirable on varmints than 243 though. If you don't think you'll ever hunt game bigger than deer buy a 243 and don't look back. If there is a possibility of game larger than deer my personal pick is 2 rifles. One in 223, and the 2nd one in either 6.5 CM, 7-08, or 308.