OK, a couple things.
If you're building a benchrest rifle from a 700 action, one of the basic and vital steps is to have the action trued. The gunsmith makes sure the barrel threads line up with the bolt, and that the bolt lugs bear evenly, etc. If you want a true tackdriver, having the action trued is a step you cannot overlook.
Having the action trued may add some cost to your project.
Most of the benchrest crowd (who do thair paper punching at 100 and 200 yards) use a much lighter bullet than a 107. More typical is a bullet made by a benchrest bullet maker (like Berger) in the area of 65 grains. There are several other small custom bullet makers for match bullets, too- Berger is one that you can find easily, and they make excellent bullets.
The benchrest folks don't usually use dies that mount in a conventional press, either. They use dies that work by hand or in an arbor press- those dies produce ammo much more slowly than press mounted dies, but the ammo will be very, very concentric- which is vital to shooting reall small groups.
Check thru the Sinclair catalog .
www.sinclairintl.com for Wilson dies. The aren't much different in price than standard press type dies, but they can help produce very good benchrest ammo.
All this stuff costs money.... you have to decide how small a group you want, and how much you're willing to pay to get it.