BUY THE BORE!!!! And learn how to judge that at a gunshow.
There are a number of books on the market that discuss the finer points. From a view of authenicity try The Collectible '03. JC Harrison, M1903 Springfield Rifle, Joe Poyer, An Illustrated Guide to the '03 Springfield Service Rifle, Bruce Canfield. Obviously there are many other excellent books available, this is meant only as a few suggestions.
The idea on Buy the Bore is cost. Stocks are availble but rebarreling is $$$$$. At a show this past weekend in Lakeland, FL, '03s went from $550 on up, some over a $1k. You have to know what to look for.
Also, get registered with the CMP, CMP Home, so you can see prices on '03s and buy some ammo, the cheapest around.