Great question and a very important one. As far as music goes, if you have a superdrive then back up everything on a DVD or two depending on how much you have. If you have all the original Cd's to the music and have not purchased anything from the itunes music store then there is no real need to back up the music files. It isn't too hard to just reimport the music from your Cd's. Someone else can help you if you want to back up just your purchased music off iTunes music store cause I don't know how to except using my .Mac account with backup software that comes from apple.
do you have a .Mac account? If so that really changes things.
what kinds of files do you create...mostly work processing and spreadsheet type stuff? Or do you do digital pics, digital illustrations, etc.? That would make a big difference on how you would want to back up and how often.
I second the comment about keeping the latest backup disc at a workplace or another location. If either place burned down you would always have a copy of everything (unless you left a laptop at your work that is the computer you are talking about backing up

) anwyay, if you don't have much to back-up then try doing a rewritable CD and buy two so you can keep one at work and have another at home to burn every so often and take to work, then bring the older one home to reburn again after erasing (which is another whole question for a later date but you use disc utility in the utility folder which is found in the applications folder)
good luck and let us know what you are backing up so we can rec. a better option that fits your needs. If you do lots of digital work that are huge files, then an external hard drive is probably your best option (but remember if you go this route and your house burns down you won't have anything so even then, a cd or dvd might work as a just in case to keep at work and burn every few months)
I backup all my documents, smaller files and computer settings/preferences online every week using my .Mac account and backup software and I also use that sofware to burn everything I want to back-up to a DVD and do that about every month or so depending on how many pictures I take of my kids or how many papers I have written for grad school.