Have all of the above.  The Marlin has a very accurate barrel bought it used but Like new for $35 couldn't pass up that deal.  Also have the savage.  Very accurate and a nice trigger.  The Marlin trigger is a bit stiff.  Have a Remington 513T.  It will go to the $300 end of the spectrum if you can find one but 1" at 100 yards is normal for this rifle and it will shoot under 3/8 " at 50 yards consistently.  Any of the above would meet your accuracy criteria.  If you truly want a tack driver at a reasonable price go to http://www.odcmp.com and look at the H&R M12, you will end up at about $300 with sights or the Mossberg 144 US, you would have to buy a mag for the Mossy, those are about $35 each, but the rifle will exceed your requirements for accuracy.  Also for true classic tack drivers look at any of the 1940s to 1950s era mossbergs.  For more modern fare, the CZ is hard to beat in a bolt gun.

Avoid the 10/22.  The only way to make it anything but a plinker is to dump money at it.  To get your level of accuracy you would easily triple the initial purchase price and end up dumping everything that came with the rifle except the receiver and magazine.