Ammunition availability for a certain caliber, along with the component availability is always a grave concern. After having dabbled in a lot of Nitro's and other less available components, I've pretty much come to the conclusion that it's of utmost importance to choose a caliber that can be found if needed on a short-term basis.
For what you may need, a .375H@H will be "ok", but in my mind, with the big ammo companies helping the situation recently, I might opt for the .416 Rigby. In fact, I know I would.
The .404, is simply too hard to find components on the short-term.
The .338 is too small in my mind to be a best "all-around" gun.
My vote-.416 Rigby----keeping in mind that you should stock components in some quantity, should they become harder to get in the future for some odd reason.