I have owned several pistols in each of those calibers, and I like all of them a lot. For most shooters in your position, I am going to say the .45 Auto is the smartest way to go. 10 rounds of any of those 3 choices should be enough for most self defense needs, but the .45 is a bigger bullet than the other 2, and has been around long enough that there is an almost endless selection of loads available. It is also available nearly everywhere.
Yes, 10mm and .357 SIG have been gaining some steam, but neither has reached the point where you could take a road trip knowing that any Wal-Mart, gun shop, range, or sporting goods store is going to have a fair selection of ammo for your pistol.
One of my biggest complaints about the 10mm, and .357 SIG pistols I have owned, is the fact that in order to get those great ballistic performance stats the rounds are famous for... You pretty much have no choice but to order the ammo from boutique manufacturers, pay shipping, and wait for it to be delivered. Even when you do this, you're most likely only going to do it for a few boxes of carry ammo, and will shoot the powder puff stuff you find locally for practice.
When you consider that most off the shelf 10mm is pretty close in performance to .40 S&W, and most off the shelf .357 SIG is comparable to hot 9mm... You aren't generally training with ammo that is comparable in feel to what you carry. And, if you carry the off the shelf stuff, you might as well not be paying inflated prices when you could have the same thing in a .40 or 9mm.
This isn't to say that you wouldn't be getting a more potent pistol if you went for a 10mm, or a .357 SIG over a .45 Auto because you would be. It's just that for most of us who have to operate within the confines of a budget, you aren't likely to spend enough time shooting the good loads through those guns, to make it worth choosing one over the .45 Auto.
All of this is assuming that this pistol would be used primarily for protection against human adversaries. In the event that you might anticipate encounters with 4 legged predators, the 10mm loaded appropriately would be my choice. And, while I like the .357 SIG... It would be my third choice of those three for defense against either type of threat.