Great choices! Ok - I'll have another stab... If I'm restricted to 3 only for the world - ever - what about

single shot .300 Win Mag - should cover most long range stuff, including sheep, goats, deer, elk, etc.
double rifle 9.3x74 - should more than adequately cover anything at short to medium range (in style!)
bolt action - .458 Lott - for DG on all continents and some specialities such as bongo and derby eland

Also covers 3 action types and ammunition should be pretty available. I'd choose the single shot for the light rifle as I wouldn't want to use it for DG. It might have oil finished laminated stock for added toughness if this is to also be a mountain rifle. I'd choose the double for the medium as I'd get to use it more than if it was only a DG rifle. Finally, I'd choose the bolt action for the large calibre for 3 reasons - I'd like a bolt rifle as one of my 3; I'd like more than one shot for DG; I'd like a laminated stock so that I could carry the rifle to Alaska and Cameroon without worrying about a fine walnut stock in the wet!

Finally, if I were allowed 5 rifles only - ever - I'd add a .223 for target shooting and a 6.5 as a deer rifle and be a happy man.... probably