I think they are all correct.

The comma is the one to use, here and in most cases, to provide additional information. The dash is used rarely, only to emphasize an insertion that is forceful, not like in this case where you are just adding the information to clarify that you mean both kinds of hospitals. Example: "That was the only time -- the single time -- that you did what I asked. (I have to use two hyphens to represent the dash, as I am typing on an ipad.) The brackets, or as we would call them "parentheses", at least in the US, could be used here, but are more often used to add somewhat incidental information or an "aside", where you make a side point that is not part of your main meaning. Example: He used an adze (a tool somewhat like both a pick and an axe) to shave off the rough spots on the wood.