Since this is a suggestion thread, this is what I'd do.
First I'd get me a Remington 700 action, by either just buying one or finding and ADL or other cheap rifle for the action. This will run you about $300.
Second, I'd get me a nice light stock with a good recoil pad. My preference would be a McMillan, but I could settle for a Bell & Carlson if money was tight. Figure $200 for the B&C.
Third, I'd get an 18" Krieger barrel in a sporter profile. It's a good barrel and you'll experience minimal POI shift as the barrel gets hot. Figure $600 for the barrel and the labor cutting it. Or you could erase the Remington and replace it with Savage and save a little on labor.
Fourth, $100 on a Shilen trigger.
Lastly, I'd top it off with a Nightforce 2.5-10X32. Figure $1500.
Yeah, I've been putting thought into a similar project too. I really love bolt guns these days. I know a guy that can put three rounds into a 6" target at one hundred yards off hand in under five seconds or pretty close to it. He really inspired me and I am going to build this rifle. I just haven't decided if I want to stay with Remington, since I already have the action or if I want to start all over and get a Steven action and go the Savage route, leaving the way open for barrel changes as I see fit.
I've also considered Bergara barrels. At $325 in a do it yourself kit, they seem appealing.