http://buildbot.orphis.net/pcsx2/index.php newest version of pcsx2 can be found here and its updated often.
digimon world 4...it should run with no major problems aside from sluggish frame rates but thats a given with ps2 games in general.
yeah, should run fine aside from the frame rate (which can affect the audio frame rate as welli don't remember how that might be fixable).
newest version of the emulator, plugins can pretty much all be left as they appear by default:
http://imgur.com/pVizIOG you may or may not have to adjust something in the video plugin settings but this game should work good enough. as for the BIOS files you'd need, i don't even remember where i got mine. but once you download the game, unzip (and unECM if needed) then click CDVD > Browse and choose where you unzipped the ISO then click system > boot CDVD (fast or full, doesn't really matter which) and it should start up and work fine.
oh, right, http://wiki.pcsx2.net/index.php/Digimon_World_4