Very important. Granted, I tend to play RPGs, a genre that tends to focus on character development, story and emotional shit. But even in any other game, if there's a huge bossfight, having kickass music in the background will enhance the experience (and your morale). Prime example below, roughly from 12:30-ish:
THE BEST METHOD to run PSX games (and everything else for that matter) is via Retroarch - http://buildbot.libretro.com/nightly/
If you have any questions on how to set it up on Windows please feel free to ask, its very easy.