On finding the right romset: The easiest way of doing this is to make sure that the one you download is labeled with which set it is from. This will make most games (60%-70%) work right out of the box if you select an emulator designed to work with that romset (see Here and Here). The remainder can usually be made to work by trying different emulators or seeking out another rom.

Basically, it is prohibitively difficult to find out which romset you have if it isn't labeled from the get go. Much easier to look for one that is marked.

If the screen goes black after a game is selected and then returns to the main menu, your emulator and rom are not compatible and you should change one of those two things.