Go 30-06. It'll do anything the .270 can do, only harder. You'll be able to kill anything you can afford to hunt with it. The ammo is cheaper and available enough and doesn't kick you into next week, so practicing is more fun. And in order to get good with it, you will need to practice. I'm a lefty myself. I shot a single shot Browning for years. I now am back to bolt rifles, right-handed of course. But still shoot them south paw