Audacity
I have digitized a few casette tapes that never made into CDs using Audacity, an opensource (and free) program which works on Macs, Windows or Linux. It has a built-in noise removal function, that might be good enough for you. "audacity.sourceforge.net" have links to some nice tutorials that you can check out as well.
Audacity noise removal has two steps. First, you highlight a section of your recording that is supposed to contain no music, just the background hiss, and have the noise remover to sample it. Afterwards you highlight all of the music that needs to be cleaned up and have the noise remover to do its magic. It worked very weel for me, but I am no audiophile. Still, I reduced the amount of noise removal quite a bit (it has a total of 8-10 settings.) Otherwise the music and vocals started sounding quite metallic. It has a nice "undo" capability, so you can try a few different settings without fear of messing up your original recording.
Sampling a five second noise section and removing the noise on a half hour recording takes a few minutes to complete on an old Windows XP laptop. If you sample longer noise sections, the processing time goes up, but I'd assume the quality of noise removal might improve as well although I haven't experimented with it too much to find an optimum length. Afterwards you export your project into WAV, AIFF or mp3.