A 223 is a little light to be ideal for hunting, depending on what you are looking to bag.
Similarly, a 308, while it is a great calibre for hunting, is a bit much if you are really going to be doing more target shooting than hunting.
Perhaps you should be looking somewhere in between, like a .270. I enjoy a 243 also, but that may just be because it is what I am used to.
Edit: you can get a number of decent new rifles for under $500. Maybe head down to a gun store and see if anything catches your eye or feels good in your shoulder.
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