Boy, advice is all over the map. Post states that you want to "reach out and touch" them (varmints) sometimes, so on occasion fair distances are involved, I presume. So, forget pistols and shotguns. You also want something compact. You may not know it, but you also want something for which you can easily (Walmart) get cartridges. I flew into Dallas last fall, and headed for a small town at 175 miles away where a friend had a ranch (and large deer). I, being brainless, didn't stop until a modest-sized town, with a small Walmart and similar stores, within 30 miles of my destination. Available - .243, .270, 30-30, 30-06 and 7mm. For your purposes, a .243 fits (tragectory, bullet weight). That said, "compact" is a bit tough. My son has a "youth" Remington Model 7, which looks like a toy but with which he nailed a bunch of deer during his early teens (now has .308). I've a Mini-30, for what reason I have no clue & I rarely fire the gun, but the trajectory is about the same as a 30-30 (over 150 yards, you're basically lobbing the bullets). A Mini-14, AR-15 and the like (.223) are certainly alternatives, but they're not much on distance either, and impact of the small bullets at longer distances isn't much good for anything but very thin skinned & fragile animals (e.g., humans, which is what the guns and caliber were, unfortunately, designed for). That said, if you plan to throw the rifle in your pickup bed or otherwise treat it rough, forget scopes, and settle for a iron sighted 30-30, Mini-14 or similar. Yup, the 25-06, .264, 6mm, 7-08 and so on are great, but are commonly used with scopes due to their distance capabilities --- and try finding cartridges at 9pm in any small town in the US. As to the 336 and so on calibers - it ain't moose you're after. My favorite rifle is a 7mm - shoots flat and long, but you have no need for such on hogs & coyotes - overkill.
Good luck, and good hunting.