You could use iDo Script Scheduler (free from Apple - go to the Applescript homepage) to launch scripts that start and stop an mp3 player at the appropriate times. Currently, iTunes is not scriptable.
I haven't tried the others.
If all you need is to start the thing by hand and then have it shut off after an hour (like a sleep function on a clock radio) then you don't need any scripting.
Just set the energy saver control panel to shut down or put to sleep the computer at a specific time. Then launch iTunes and have it start playing randomly. Then go about your business. At the specified time the computer will shut down or go to sleep and the music will stop.