Hmmm...
Having built more than a few Sub MOA rifles such as: M1D, M1NM, M1A NM, M1903A3, Mini 14s, Remington 600 and 700s, a bench rest rifle made from an XP100, a 45/70 Remington rolling block, and three SKSs I won't call my self an expert on sniping but I do know how to build a damn fine rifle. There are lots of great rifles out there but I always thought that there is no such thing as a "best" sniper rifle.
Let me explain my reasoning. Honestly if I wanted to make a long distance kill I'd use a use a tank gun. I've hit troop targets out to 3200m with 105 sabot from a M60A3 at night. If I wanted to do something close I'd use a T/C Contender in .22 Hornet. Close and quiet a Supressed 22lr bolt gun. What I'm getting to is that you use the best tool for the job.
It's the shooter that makes the gun great. I built a super tight **** hair from not closing chamber 308 win. remington 700. One of my best guns ever. Brand new match reamer that cut the fluted Hart barrel like butter. I had trued the action so everything was in alignment. Pulled every trick in the book and a few not in it on it. This thing cut a single ragged hole with 5 rounds in targets out to 300 meters all day long and the price tab was $4K parts and labor in "92". I give to the customer and two days later he's on the phone bitching at me. I have him come in and he brings in a target that looks like it was shot with 00buckshot at 60 yards. We take the gun to the range after I cleaned it. Both me and my boss shoot it with factory ammo. Flawless. The customer looks at us like it was some sort of trick. He gets behind the butt loads his own special loads and can't hit shit. I'm a good shot but that gun made me look great. Give a great shot the same gun and look out.
I will say this if the gun is built on a Remington action by a good smith you can't go wrong. My caliber choice would be .338 Winchester Magnum that headspaces on the neck not the belt. The .300 win mag and 7mm rem mag are nice but the 338 is king.