Being new to hunting, scratch the .223. The .308 is probably the best bet, and has a wide array of factory ammo readily available.
Personally after a 10 year hiatus from hunting (or even shooting at all, because of international travel) I came back into the game with .243 because that was the only way to swing the purchase "yes babe you will be able to play with it also". Well she never once ended up shooting with me. I have since upgraded my partner but the little laser beam Browning is still in the stable.
Ultimately depends on the usage you require. Where you hunt, what you hunt, and how confident you are with shot placement.
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