I second Volquartsen as a 10/22 upgrade. "Best bang for the buck" not a primary requirement, also consider Anschutz - long known for match accuracy in 22s. Here is one link:philthygeezer said:
http://www.championshooters.com/Anschutz.htm
You can search for others.
If you are looking for centerfire, there are many to consider. A "guarantee" of moa performance, you will generally have to spend more than $1000, but should find many that fit the bill between $1000 - $2000 and a little more. Yes, there will be some factory rifles from Remington, Browning, Winchester, Ruger, Savage, etc. that may come in under one moa for $400 to $800, but that will just be lucky IMHO. A Remington 40X from the custom shop would be one factory rifle I would trust to deliver sub-moa in many calibers. It comes with a factory test target.