You're talking about a custom rifle, at standard hunting rifle prices. If I were you, I'd want a Remington 700 BDL Varmint in 7mm-08, .260 Rem or .308 Win with a 6-24X +/- Leupold. However, even that will set you back more than you thought.
Next down might be a Tikka T3 Hunter in .308 Win, with a 4-12X Leupold. Accuracy potential is pretty much there, but lacking target-quality repeatability, due to stock forend shape and heavier weight that makes shooting longer strings at the range more comfortable.
Maybe, get a sporter rifle now, and get a Mcmillan or other long-range target rifle stock for it later?
Maybe just buy a rifle that suits more of your shooting needs now, then buy another rifle to hunt with later?
People are like rifles. Some are tried and true, having great eyes, personality, and fun to be with. Others never seem to hit the mark with you. Still others go off half-cocked. Still, it's nice to know most of them.