Though I've never shot one, I'm taken to understand that the 10mm is an incredibly versatile round. From concealed carry to a lot of hunting/outdoors applications it seems to fit the bill.
The only downside is the cost, as I understand it, 10mm can be quite pricey.
Easy..10mm.
As has been said before, it can pretty much do it all if need be. Besides being a great choice for "anti-personel" tasks even at extended ranges, it makes a great wood defence or medium range hunting round with proper ammo. Its comforting to know that your sidearm can be pressed into rifle duty if need be.
I love autoloaders, but if limited to one caliber, the one I would choose is not listed. .357 magnum. It can take everything from small game, whitetail deer, and serve as a defensive sidearm.
I'm assuming a pistol's most demanding purpose is for self-defense because that is what I would want it for (against bears, mountain lions, big apes
That said. 10mm
We can debate the pros and cons of various calibers and this has been done in hundreds of threads here. Bottom line is the most power in a pistol that is commensurate with practicality for my hand and ability to carry. The .50 AE Desert Eagle is impractical.
I wish Sig made a double stack 10mm.
Seriously, I would want a "hunting caliber" for hunting deer if necessary.
The .357 Sig would be a second choice.