My fav all around cartridge is the 280 Remington. Mine launches 145gr LRX's over 3,000fps, loves 175gr partitions too. Nothing in NA I can't effectively take with it. Lethal, moderate recoil, plenty of range, no magnum muzzle blast. Suits me well. Plenty of ammo available too, but if that's a concern, a 270 or 30-06 are similar stable mates.
My fav hunting round is a 25-06. Pole axes medium game and with the right pills is lethal on elk. If I was just starting out, I might very well develop a relationship with a svelte 6.5CM and keep a 30-06 around for anything mean or larger than an elk.