The one drawback to semiauto's is their more limited bullet selection (many won't be happy with more than 150/165gr). Otherwise they're fun, some can be accurate (PTR91, AR10-variants with $$ invested), and cheap to feed.
For a semiauto .308, look into the Winchester SX-AR (AKA the FN-AR
). It's a rebuild of the classic Browning BAR design, with a few modern goodies to it. Built as a hunting rifle, less of a battle rifle.
As mentioned above, the PTR-91's have been getting good reviews, their only drawback is poor chamber fluting, so they can be picky eaters. But, if you're just hunting, why not feed your gun the best anyways?
Or, grab an AK, five 30-rounders, and who cares if you don't hit the deer on the first shot, or third, or eighth, or 11th...well, you get the idea...
Just my $.02