There are retaillers who specialize in such things. While it may not be as rock bottom priced as you may get at an auction, the logistics might be better. In my area there are a couple of major ones - I bought my parents a computer from one of them for an amazing price.
I would suggest you look for the "corporate" grade computers, not the ones built for the home market. Corporate computers usually have better cases/power supplies/components. This is generally what comes available at these retaillers as they buy in bulk from companies who are renewing their PCs.
You will save yourself much headache if you can get 30 identical PCs. That way you can create a ghost image for them, and instead of troubleshooting issues, you can instead wipe the drive and restore from the ghost image. Trust me having taught in a similar situation, that was something that caused me much pain - students apparently feel they can risk doing anything and everything on a classroom computer.
James