Help playing audio – what's the best practice?

I’m very new to the WordPress/website world but I have successfully created a website for an audio recording project. The website has a lot of streaming mp3 files. They range from 1 min to 2 1/2 hours. I’m using the Twenty Ten theme and uploaded the mp3’s very easily using whatever the default settings were (I think it uses QuickTime). When you clink the link you are navigated to a new window with the player which appears very simply as a single line and nothing else in the window. See below.
‘https://02d17c6.netsolhost.com/ulyssesroot/listen/demo/’

I am wondering what the best practice is for playing audio files on websites. This is not a blog. I know a lot of sites stream within the browser’s windows (as my currently does) although I know others open these files in separate programs, iTunes, Windows Media Player etc. Some of these recordings will be long so it would be nice for people to be able to continue navigating the website while listening. If I continue streaming in the browser window, is there a way to include an image with the player? Is there a way to give people both options, either listen on the site or open a new program?