I am really liking my remington 700p in .308 with some atrs love. It's my first 'precision' or 'long range' rifle and I really think you'd be hard pressed to beat it for the money.
When I step up to the next level it's either going to be something like a Sako TRG-22 or a full custom build ontop of my existing 700p (trued, match barrel, bottom metal, mcmilan a5 or aics) and you're easily doubling the investment at that point.
Mine is shooting well under 0.5 moa and I am *NOT* a good shooter. I am just starting out!
I'm new at this but my advice would be that pretty much any higher end factory rifle (rem 700p, savage 10fcp, tika tactical, etc) are going to be better than you out of the box. As a shooter we are the weakest link. Every shot I've messed up so far has been entirely my fault.