Right at the $300 mark is the Stevens 200 by savage. I've seen them for sale for $299 and $319.
They are plenty accurate out to 200 yards...and they are about the least expensive rifle you are going to find...new at least.
I suppose you could buy a Mosin Nagant which is what the Russian Army used between 1880s and up until sometime after World War 2. In the 1950s they put millions of them in warehouses, and now they are selling them off. You can get one for $100, and it is pretty frigging weather resistant simply because it's already a weatherbeat old gun.