Unmodified JJ2, regardless of version, should run fine on pretty much any configuration of Wine.

If you use JJ2+, then it will either work perfectly or it will have really weird problems or it will not work at all. For the "really weird problems" bit, try setting your Wine sound driver to ALSA, starting XMPlay in Wine and playing a song (put it on repeat), then set the sound driver to OSS, then starting JJ2 - you'll get no sound but if you don't do this then it just crashes every time. Also trying to use the plus injector during a single player game will make gravity disappear.

No, seriously. Also I think it runs perfect on really old Wine versions (1.1 or so), so I guess you could try that.