RE: Paper Puncher
For a paper puncher, I would suggest the .223 Remington round over the 22-250. Nothing wrong with the 22-250 at all, but a .223 is slightly easier to shoot accurately. The .223 is also cheaper to shoot, whether it be factory ammo or reloading. Also, milsurp ammo can be had very cheap, and for $20 worth of milsurp ammo you can shoot just about all day. All else being equal, the .223 would be my choice, just for the shear economical aspect of shooting it. Also the .223 is extremely easy on barrel life.
Probably, the best platform to build a cusotm rifle on is the Remington M700. Not neccessarily becasue it is the best, but because it is so popular and has an almost unlimited amount of accessories avaliable. The Rem. M700 has tons of after market or custom, stocks, triggers, safeties, magazine/floorplates, scope bases, barrels, recoil lugs, and magazine followers for it, in many different price ranges.
If I were to buy a heavy barreled rifle, it would have to be a Savage in .223 single shot bolt action, with a 26" heavy stainless barrel, with a pillar bedded laminated stock, model 112BVSS. These rifles are notorious for shooting itty bitty groups. When punching paper, a single shot is all you need. One thing about the Savage is that the trigger is no the best. The first the I would do, is get an after market trigger, like a Sharp Shooter or Rifle Basix trigger. These triggers easily be set 1-3 pounds. Also the Savage has a unique feature in that the bolt head floats just a little. This allows the cartridge to center itself in the chamber, which adds just a tad to accuracy.