Perhaps a special purpose hog gun like a lever action Marlin in 45/70 or 450 Marlin. No real need for optics, but you could install a goo quality low-power fixed or variable and still have over half of your budget to spend.
Personally, I don't have a use for high-dollar guns. I like them as much as anyone else, but that's not a priority for me right now. My guns have to earn their keep in the woods.