As you can see from the plethora of answers, your criteria were open enough that there are lots of solutions that fit. Pie plate at 300 yards is about 4 MOA which anything decent should be able to do.
There are dozens of bolt guns that will fit the bill. You don't need a Remington 700 5R (which, with optics, would break your budget). My Remington 700 SPS Tactical ($600) will easily fit your accuracy requirements. It's not mag fed but finding something equivalent that is isn't hard.
For semi-auto's two pop into my mind;
The FN FNAR can be had for right at $1000 now if you look around. The folks I know who have them say they are very accurate and fast shooting. Only complaint is they have to clean from the muzzle and magazines can be pricey and hard to find. If you can't find one look for the Winchester SX-AR which is basically the same thing in camo with less rails and slightly cheaper.
A PTR-91 (HK91 clone) can be had for about $1000 and also fits the bill. Not as accurate as the FNAR but magazines are dirt cheap and common. Get a MFI low profile rail for the reciever and you are gtg.
Or do something crazy. Get a cheap M1 Garand ($500) and send it to Shuff's to be rebarreled in .308 and add a scout scope rail (under $500) - although that might push your weight limit.
There are dozens of bolt guns that will fit the bill. You don't need a Remington 700 5R (which, with optics, would break your budget). My Remington 700 SPS Tactical ($600) will easily fit your accuracy requirements. It's not mag fed but finding something equivalent that is isn't hard.
For semi-auto's two pop into my mind;
The FN FNAR can be had for right at $1000 now if you look around. The folks I know who have them say they are very accurate and fast shooting. Only complaint is they have to clean from the muzzle and magazines can be pricey and hard to find. If you can't find one look for the Winchester SX-AR which is basically the same thing in camo with less rails and slightly cheaper.
A PTR-91 (HK91 clone) can be had for about $1000 and also fits the bill. Not as accurate as the FNAR but magazines are dirt cheap and common. Get a MFI low profile rail for the reciever and you are gtg.
Or do something crazy. Get a cheap M1 Garand ($500) and send it to Shuff's to be rebarreled in .308 and add a scout scope rail (under $500) - although that might push your weight limit.