Sorry to say but, benchrest is way out of the league of an old mauser action now a days.
A decent starter bench gun would be the Savage 12BR in 6br http://www.savagearms.com/firearms/model/12BENCHREST
You don't see many factory actions on the lines today unless they are in a factory class. If someone is using a factory remington action more than likely it is blue printed and sleaved.
Most bench guns use short squat 6mm cartridges like teh 6ppc, 6mmBR, 6dasher stuff like that. You can use a long action like the Mauser but you are losing accuracy because of the long action and the flex.
Benchrest is a whole different monster. I know of a small but growing benchrest comp called Ultimate Benchrest
or UBR. This uses targets based on the diameter of your bullet.
If you are real serious about getting into benchrest head over to benchrest central and take a gander at the used rifles.
If you don't want to spend $2k+ just for a rifle. Better stick to the factory class and start with the savage above or Remington 700. You might not think so but there is a lot of time money and effort that goes into benchrest shooting. Many buy custom made bullets along with custom guns. Rests that weigh 30#+ and bags.