For your budget, you can get a nice Manner's stock. Go to their website and pick out your favorite.
Buy yourself a used Remington 700 BDL action off gunbroker, or at your local gunstore/gunshow. If you can't find the action by itself, look for a used hunting rifle. You can find good deals if you get a beat up hunting rifle that has been carried on many hunting trips and abused, but not fired much. You should be able to get one for $300-400.
Take your action and stock to your gunsmith. Talk with him about barrels. All of the high quality custom manufacturers mentioned earlier make excellent barrels. Arguments could rage for years over who is better. All make barrels capable of shooting far better than any shooter in field conditions.
$400 for a barrel, another $500-600 for smith work: Blueprint action, custom ground recoil lug, cut chamber, install and headspace barrel, true everything up, bed and float action/barrel into the stock. Then refinish everything. Save some money here and don't go for a crazy custom finish, just get something cheap and weather resistant. If you want it too look good, do it yourself with a can of Krylon spray paint. Also have your smith adjust the factory Remington trigger. A properly adjusted Remington trigger can be just as nice as a $200 aftermarket drop-in trigger.
If your smith knows what he is doing, which is the most critical aspect of the build, you should have yourself a .5 MOA or better rifle, that will most likely shoot much better than you.
Next step, GO SHOOT. By the time you can shoot nearly as well as the rifle, it will be time for a new barrel. By this time you will know exactly what you want and can rebuild the rifle from there.
