The gun was originally chambered for 9mm Largo. The 9/38 on the gun indicates that when it was surplused from government service, it was modified to fire both the 9mm Largo and the 38 ACP ( NOT the 380. The 38 ACP is a now obsolete cartridge which was the forerunner of the more powerful 38 super.)
Pistols chamber for the 9mm Largo CAN fire a number of 9mm rounds like the 9mm Parabellum or 380 ACP because these rounds are shorter than the 9mm Largo. But this is a very bad idea. Instead of headspacing properly, the round is simply held in place by the extractor. This is very hard on the extractor and , if the extractor does not hold the casing perfectly, the bullet may not be exactly lined up with the bore. In addition, loads like the 9mm Parabellum have higher chamber pressure than the 9mm Largo. This is something to remember since steel treatment in the 20's were not what they are today, reducing your margin even more. All in all, firing non 9mm Largo rounds in a 9mm Largo is not IMHO worth the risk.
Yes, 9mm Largo is rare and expensive, though possible to find.
Yes, a Model B which is made for 9mm Parabellum would be a better idea. A BM ( Unfortunate choice of nomenclature, M indicates small, a Commander size gun) would also be good. A load of these came in surplused a year or two ago. I paid $165 for mine then. You might look for one of these second hand.
Parts for any Star pistol are hard to find and expensive. The Company is out of business. You have a much better chance of finding parts for a Model B or more recent gun than a Model 1922. The firing pins are especially vulnerable to breaking. Never dry fire one without a snap cap.
MY BM is a very nice gun, very pleasant to shoot in 9mm, which is not surprising with all that weight. It differs from the 1911's in the lack of a grip safety and in the mechanical safety, but the "feeling" is the same as a 1911.
Hope this helps- conwic