Hello
I a weighing whether I should purchase either a 1903,einfield, Mosin Nagant, or a K31.  I plan on instaling a scope and trying to obtain the maximum accuracy with the least amount of money.  Which rifle would you all recomend.

Well, the '03 and Enfield (1917) would cost you probably upwards of $500.  A .303 British Enfield would be less expensive, but the non drill/tap bases suck for them.  The Mosin would be the cheapest, and cheapest to feed, but scope options might also be limited.  

The K31 would be the most accurate of the bunch.  There's a good reputation clamp on scope base (St.Marie is the name), the only oddity is that it offsets the scope to the right, as the rifle feeds and ejects directly out the top.  With this setup, you can still use the irons if you need to.  Alternately for $70, you can get one of Darrell's Scout Mount scope bases that goes on in place of the rear sight.  No tooling or machine work, so you can swap back.  Put a decent ~4x pistol scope on it, and you have a nice setup right there.  

accuracy for the least amount of money would definatley be the k31, accuracy and a high degree of collectability would be a finn mosin m39 for $160-$200

excelent, I believe I will go the K31 route.  Thank you for you advice.  Pics will be posted when I purchase