Hi LuckyMaroon!
As Bernhard said, you can go with David-Laserscanner and structured light for eye safeness (no laser). If you already have a beamer and a web-camera (or better a Canon-DSLR or even better a machine view camera) then you only need a license for 329 Euros ( Pro USB Edition) to start with a structured light scanner. You have to do some DIY to built the scanner, but I think that is interesting to the kids too, look for advices at the forum of David Laserscanner at
http://forum.david-3d.com. There is also a complete solution for 1993 Euros
https://ssl.david-vision-systems.de/shop/product_info.php/info/p124_DAVID-Structured-Light-Scanner.html.
Another possibility is photogrammetry. A good point to start with is the free VisualSFM (for noncomercial use) see
http://ccwu.me/vsfm/. For working with the point clouds you can use free software solutions like Meshlab
http://meshlab.sourceforge.net and CloudCompare
http://www.danielgm.net/cc/ or of course your edition of Rhino and ZBrush.
If you want to spent some money for photogrammetry I could recommend Agisoft PhotoScan. The standard version for educational use costs only 59,-$ and the professional edition for educational use costs only 549,-$.
You can start with normal point-and shot-cameras.
Hope that answers some of your questions
Best Karsten