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.
I have a very strict gun control policy: if there's a gun around, I want to be in control of it. - Clint Eastwood