I suggest a Savage Weather Warrior. It will come in well under your budget and leave you some extra money for the scope. I would suggest another caliber as I believe .308 and .30-06 are slight overkill for deer/boar in most situations, but it will open up a whole new can of worms. All I'll say is the Weather Warrior is also offered in .25-06, .260 rem, 6.5 creedmoor, .270 win, and .270 wsm, to name a few.
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