ForJJ2, try some different settings like turning off DirectSound or toggle Hardware Accelleration. Or try 8 bit mode to see if it makes a difference in playability. It's all done from the options menu (or menu bar in windowed mode).

It might me a good thing to fully avoid the Alt key in Windows games these days, it triggers the menu bar and could trigger a lot of other actions if accidently pressed together with other buttons. Try using Z for jump, X for shoot. Works comfortable for JJ2!