First of all, it would help if you had a better idea of just what type of benchrest shooting you want to pursue. Just shooting from a bench and attempting to hit paper or steel at 1,000 yards can be a challenge by itself but it's a tad harder to shoot small groups at 1,000 yards. Sure you can use most of the hunting rifles available to shoot at paper at 1,000 yards but shooting it for small groups is a different game.
While an M98 Mauser might be a good candidate for rebarreling it might need some consideration as far as shooting at 1,000 yards. The M98 models usually have a slower lock time than the actions which are chosen for true benchrest shooting. It's also a little different loading a true controlled round feed action for single shooting at long range targets.
Basically yes. Commercial FN Mauser actions are large ring by design (1.400" diameter). Generically, different large ring barrels might fit your action as far as the thread form is concerned but the headspace may need to be adjusted.
The FN and the 'large ring Mauser' barrels are the same or very similar thing. But the #4 McGowen is usually considered to be a sporter hunting style barrel 0.650" at the muzzle, not a benchrest type barrel. But no one says you can't shoot it anyway then take it hunting. Your trigger choice will need some consideration as well.
I wouldn't waste time or money on a Ruger.
The Remington M700 is one of the most common used actions for many beginners getting into target shooting due to the overwhelming number of accessories and stocks available.
Enjoy the process!