Short of Milurp stuff, or carbine calibers(.223, .357, .30/30) ..... it does not get much cheaper than .308 WIN.
There are good deals on lefty guns out there, particularly used ones on consignment racks.
If you want a GP rifle ..... .308 is good caliber choice.
If you want to be able to afford to shoot more, of ANY caliber, handload.
It is not rocket science. Follow simple steps, diligently, take no shortcuts, understand what it is you are doing, and you can cut the cost of most centerfire ammo in half, and make better ammo, in the long run. The key is that last part: The Long Run. It's not an instant gratification thing, and many people don't have the attention span for it.
TheGolden Rule of Tool Use: "If you don't know what you are doing, DON'T."