Well, I love the 7mm Remington Magnum. Good for antelope with 120s, deer with 140s, and it has quite a reputation for elk. Just depends if that's all the bigger you're wanting to hunt. Nothing wrong with a 270, 280, or 30-06 either (of which I always wanted a 280), and numerous other cartridges. The good thing about shooting a 28 or 30 cal is the bullet variety favoring elk, without giving up anything for smaller game.

The 223 is a perfect yote cartridge. Since I handload, I'd go with a 22-250 myself. Keeps ammo cost about the same with the ability to make things hot for a flatter shooting gun, and shots can get long from the yote hunting I've done.