Welcome!
There are a few things that Are pretty neat. I'm not sure what you've already got stuck into, but here goes anyway! There is heaps of info on each of these things all over the forum, and don't be afraid to ask questions!
For making new objects, I've used two apps, google sketchup and inventor fusion. Sketchup is great because it has a fairly shallow learning curve. Inventor has a bunch more features, but isn't quite as easy to get your head around. Sketchup needs a plugin to export to stl, inventor has it built in. Both apps are free for personal use, you might need to look into licensing for educational use though.
Solidoodle recommend using pronterface and skeinforge, but there are alternatives out there that are probably better for your use. Repetier host is great. It is a hell of a lot easier to get your head (and your students!) around, and integrates with both skeinforge and another slicer called slic3r. Slic3r is significantly quicker than skeinforge, so in a classroom situation, it'd be much better. Repetier host also let's you quickly switch between multiple slic3r settings, so you can easily have options for different layer heights, support settings etc. it will take a bit of setting up, but once it is going its great.
As far as general info goes, there is heaps on here, and there are both the official wiki and soliwiki to visit. If there was just one page you could read, for me it would be 'what should I not do?' On the official wiki. I'm pretty sure I've done each one of them before I found the page
Anyway, welcome to the community!