If you cannot use GarageBand, then Audacity is the way to go. When you save the mp3 file then uploading is a doddle.
Yep. Audacity or Garageband.
I must say that since you're a teacher, Audacity would be more useful for the students as there are both PC, Mac and Linux versions (So all of them can go home and use it if they want to, no matter what operating system they have) and that it is like some of the more professional software (I went to work at a radio station for my work experience and they use this system that uses an audacity-like editor. I can't remember what it was called but it was part of a full radio broadcasting suite, so I wouldn't recommend it anyway).
Garageband is more intended for recording music - not putting together audio. However, if you're planning on using samples and adding sound effects, Garageband will be better for doing that as you use a drag and drop interface... but I advise Audacity for audio editing too as you can normalize audio, remove background hums and so forth.
Audacity:
http://sourceforge.net/projects/audacity/
I recommend you use Audacity for actually recording the audio, then import into Garageband for mixing effects in and putting in other parts of the show, etc.
That's how I do it (Although I record over the web so I have a few extra bits to do - but cutting out those bits, that's what I do).
If you have any questions, please ask
I hope this works out for you - and on a plus side, both Audacity and Garageband are free (well, technically Garageband is free but you've got to own a Mac) so you won't go over any budgets assuming you're using Macs anyway

If you're using Windows (Although it's unlikely considering you're posting here) then I'm sure we could point you in the direction of some software... after all, there are some pretty experienced people here!