I don't know if there are any .22 Short firearms in current production. Any .22LR should shoot .22 Shorts (though you may experience some failure to feed / eject problems in semi-autos). Actually, I have an old bolt action rifle with an adjustible magizine for .22 Short, Long & Long Rifle. And when I bought it over 30 years ago - you could get all three types of that ammo pretty easily.
It's my understanding that there were really two purposes for the .22 short:
1. For use in ultra small semi-automatic pistols popular in the early to mid 20th century.
and
2. Competition shooting - with target shooting specific rifles & handguns.
Now days, it's very hard to find .22 Shorts, and expensive (same with .22 Longs). There is plenty of .22LR ammo out there that ranges from average to superior quality. So there really isn't much need for Shorts or Longs among the general shooting public. However, if you run in those circles were such "unusual" ammo is used - those folks would likely be better reference sources for advise on the best firearms chambered specifically for it.