For a complete custom project, me personally (everyone has their own opinion), I would go for a cheap used Rem 700. Millions of aftermarket parts are out there to completely customize it the way you want it.
As for the caliber, if you were going to build a .260 Rem or something along those lines, and use long heavy VLD bullets for long range shooting, building the rifle on a long action would be something I would look into. That way you can use it as a repeater, by being able to utilize the extra length from the long heavy bullets, but still use the magazine to hold more rounds, instead of having to shoot it as a single-shot. And it doesn't require any extra gunsmithing work, or any special parts.
But, if you wanted to keep it as a short action, Wyatt's Outdoors makes extended length magazine boxes and followers that you could always have the gunsmith install at the time of the build that would allow you to basically do the same thing as mentioned above, but in a short action frame.
