What I WANT to choose and would choose are differe different. The real question boils down to your budget, and the number of elephants you plan to hunt. Do you value chance to hunt an elephant or the entire experience?
1) Whatever 375 or other DG rifle you currently have with irons or lower (sub 3) power scope is currently on it. Shoot a quality solid (Woodleigh, Swift, Barnes, Hornady, Norma). This plus a Tuskless is the most economical way for anyone to experience an Elephant Hunt. Since your costs are the hunt and whatever ammo you might need to buy or load.
2) For someone who might want to hunt a couple Elephants or wants an excuse for a new rifle; a Bolt Action in 458WM, 458 Lot with irons and/or a 1-4 or 1-6 type optic. As
@Philip Glass mentioned in another thread LOTS of PH’s use this set-up (mostly with just irons) including a lot of the well known DG PH’s in Southern Africa. An iron sighted Mauser or Mauser variant (M70c CZ, BRNO, Whitworth, etc) has been the workhorse of Africa for awhile. A 416 Rigby, or 416 Remington wouldn’t be a bad option here caliber wise. Again shooting quality Solids (Woodleigh, Swift, Barnes, Hornady, Norma). I think you could have your complete set-up with plenty of ammo for $1,500 - $4,000 if you shopped around and went with a Leupold, Eotech or Trijicon scope over a more expensive Swaro, S&B type optic.
3) For the hunter who wants to chase multiple Elephants, and Dangerous Game or values the nostalgia & experience a Double Rifle in one of big bores. Proper fit is more important than caliber if you’re looking used. I’d pick Iron sights and same quality solid options (Woodleigh, Swift, Barnes, Hornady, Norma). There are some who would pick a RMR type red dot. Once you get to this option (even with the most economical DR options) you’ve likely invested almost as much in your gun/ammo/practice as you will for a Tuskless or Management Bull Hunt. Had you picked Option 1 you could’ve done 2 separate Tuskless Hunts, or a Trophy Bull. Once you start stepping up in manufacturer name you’re into similar pricing as an exportable Trophy Bull pricing for the all-in cost of the hunt.
What I WANT is an old Pre-War British Double in any of the old nitro express calibers 450, 470, 475, 500/460, 500, 577. All rifles would solely have irons and shooting something like Woodleigh or CEB Solids with a hand worked load. I’ve debated selling one of my doubles to fund an Elephant Hunt. I’ve also debated selling both doubles to fund part of an old British Double. Again the question is what matters more to you, doing the hunt, or how/what you hunt with?