RE: need a high powered rifle
For that price I would say an H&R centerfire, you still might go over that price if you want a good scope. Heck a good varmint scope might cost you that much.
The only down fall is the H&Rs are a single shot, the up side is you can have it fitted for different barrels in centerfire and shotgun.
However I do like the savages. I also think the 243 or 25-06 would work really well.
Paul