It technically shoots two calibers, .357 magnum and .38 special.
If you want to be really technical, both .357 and .38 Special are the same caliber, .35...
They are different cartridges, but the same caliber.
Caliber denotes bore size (and also barrel length in artillery) but it is common American usage to use the cartridge name as the gun's "caliber" so its easy to get confused.
Use whatever you're going to be shooting most.
Adjust the sights to the ammo.
This is the most practical answer.
Unless you are using it for home defense or self defense. Then you zero it to your expensive hollow point "war loads" not your cheap practice ammo.
there is a point to this, if you are only using the gun as a self defense piece.
However, the beauty of adjustable sights is that they move, easily, and can be moved, and moved back, repeatedly.
What matters is that you shoot both your defense loads and your practice loads and determine how much (If any) difference in point of aim vs point of impact there is.
At usual defense ranges there may not be much difference, or there could be a large difference, each gun and ammo combination is a rule unto itself about that. Usually they will be pretty close, but you might have an unusual situation so you need to shoot them both to verify what you have.
Once you have the gun sighted in "dead on" for one load, shoot the other to see how far off (and in what direction) it is. Then adjust the sight for that one, COUNTING the clicks and direction it takes. Make a note (I suggest you write it down) of how much you change the sights for each load.
IF, for example, you sight magnum load dead on, and then learn that its 3 clicks up and 2 left to be "on" for .38s, there you go, make a note of that and keep it somewhere you can find it, in case you forget.
Once you are sighted in for one load, make a reference mark, such as a thin stripe of contrasting color (paint, nail polish, Sharpie ink, etc) that goes over the adjustment screwhead and the sight body so you can see when they're lined up for your chosen load. You only need one mark, it fits lined up you're sighted for "A" if not you're sighted for "B". If you're anything like me, you WILL forget which load you last sighted in for, unless you have a witness mark of some kind.
Having sighted in for both, with a way to know which is which and what the difference between the two is allows you to change back at forth at need with just a proper fitting screwdriver.