I started with a Rem700 VTR (the one with the funky triangular barrel) with the cheapy Hogue stock (that I still like the look of honestly):
Took my first pig with it. Got a (used) replacement stock, changed the optics, shot it until I wasn't happy with the performance, swapped the trigger out, sent it to GAP to have them work their magic on it, took some classes, changed the optics turrets, repainted the stock skins, got some muffler love from tsconver when I moved here, and now it looks like this with ~3000 rounds through it:
Same bipod.... sometimes I'm cheap (and the AICS bipod that came with the stock sucks, not sure if it's just worn out or if they're all wobbly like that). It's kinda big and heavy to hunt with like this, but it is just a Rem700 under all that crap, I could swap it back into the Hogue stock and knock the can off and go right back into the field.
My point is, you can start with something stock and in budget, and then if you end up liking it you can just go nuts over time and turn it into anything. That seems easier, or was easier in 2008, with the Rem700 vs. most other stuff out there.
Just for fun, a picture of me learning to drive it back in the day before I discovered krylon:
Oh, and those that say you can't do 1000 yards well with a 308, or go over 800 yards with 168gr bullets, we were all shocked when I was hitting 1100 and yards with 168gr handloads at Bang Steel. Now 1200... yea, that wasn't working so well. But given the right combo of environmental factors you can have some fun with the lowly 308 out of a Rem700. Of course tsconver was putting us to shame at 1200 and 1400 with his 300win mag, but whatever man, whatever.