But what is 9X19mm or 9mm Luger or 9mm Parabellum?
All the same thing. But do not get confused with 9X18, or 9MM Makarov. they are different rounds, and not comparable with your gun.
For general range shooting I have found Winchester USA bulk (100 rounds) to be acceptable. Also referred to here as WWB, or Winchester White Box. Full Metal Jacket, or FMJ as it is known is perfect for range use. You don't need to spend the extra money for hollow point ammo for range ammo. Some consider steel case
ammo, referring to the casing itself, not the bullet jacket to be detrimental to the extractor on a gun. The steel that the case is made from is much softer than that of the extractor, and shouldn't cause a problem. However, my experience with the cheap steel case ammo is that it just isn't as good of quality all around with many malfunctions being experienced. Others may have a different opinion.
You may find that different bullet weights and designs may work better than others in accuracy, and function. So try several to see what your Sig likes. Guns do have preferences on ammo sometimes.
Also, for range use there is no reason for ammo marked +P which is loaded to pressure levels above that of the standard for certain calibers. If you do decide to use your pistol for home defense, or CCW you will need to practice with what ever defensive ammo you chose to use for that purpose.