You can use the built in HTML5 Player, it's super easy. You'll have to use both .mp3 and .ogg though, because different browsers can only read different formats. You can also use .wav if you want to. There is no compromising quality here, and no flash! Though you can include some code so that it loads a flash player "just in case the file wont load". I use it on my site.
Code:
<audio controls preload="auto" autobuffer>
<source src="mysong.mp3" />
<source src="mysong.ogg" />
<!-- now include flash fall back code here -->
</audio>
This will use the browsers built in player. Works wonders. You'll have to use one instance for every song though. No playlist feature yet. But it's great imo. Gives room for a little description under each song
It looks different depending on your browser. Each browser has their own design of the inbuilt player.
The site is under heavy construction, and is just filled with nonsense text. It's not for viewing by people, and I wouldn't show it to potential clients. Needs some graphics and stuff