Put some consideration into the Remington 700 SPS Varmint.
Remington Model 700™ SPS™ Varmint Specifications
They make left-hand versions in 22-250, 223, 243 and 308. I personally have a 223 and 308. The .223 is bone stock and shoots .5moa with factory 50grain hollow-points. I would agree with an earlier post that the 223 is a great caliber but at 450 yards wind drift gets to be an issue. 243 would be my recommendation for you. The 243 has much less wind drift at the longer ranges and you could use it to hunt deer. (as an FYI, I chose the 223 primarily for my 12 year old niece to shoot and she has no tolerance for recoil - if it was up to me, I would have gone with the 243)
The SPS Varmint is a great platform to begin a build. It will probably shoot well right out of the box. Because it's a Rem700 everyone works on them and makes parts for them. You could trick the rifle out however you like. That's what I'm doing with my 308 http://www.longrangehunting.com/foru...k-rifle-43510/
They are also relatively inexpensive. I bought both of my rifles for $550 each. That would leave you with $250 for a scope. Nikon Buckmaster would be a good choice.