Re: 375rum or 458 lott
A .338 RUM would probably suite your needs better, but if you want a big bore the 375 RUM would be the way to go.
I dont think that the .458 Lott is anywhere near fast enough to be a long range rifel. The .416 Weatherby or .378 Wby may fit the bill, but you need a Wby or Sako action for those two.
If your building on a Rem 700 action the .375 Ultra is the no brainer. Go with a 26" tube minimum.