Re: 338 win or 338 rum
If you want a repeater, you will need a full length Mauser action. There were some Mauser 98 guns chambered for the 375 H&H Mag but they were modified bu grinding away some of the bottom locking race. The 375 H&H round is fairly low pressure compared to the RUMs so it's not advisable. The Rem 700 is easy to find as is the Winchester 70 for full length high pressure rounds. There are also a lot of custom actions that will work very well.
On the other hand, the 338 Win Mag is a good choice for the 98 Mauser as is any of the standard length magnums (.264 Win Mag, 7mm Rem Mag, 300 Win Mag, 338 Win Mag). I thought about building a 330 Dakota on a Mauser 98, but the slight velocity gain was not worth the extra cost of custom dies and brass.