It is cheaper to upgrade. In the United States, the upgrade is $79 whereas buying new is $149.
There is no student or teacher edition of Lightroom 6.
Here is how to purchase Lightroom 6: http://laurashoe.com/2015/04/22/video-tutorial-on-how-to-upgrade-to-lightroom-cc-6/
We don't have a student/teacher edition of Lightroom 6.
The perpetual version of Lightroom 6 upgrade is available - http://shop.adobe.com/DRHM/store
You may wish to consider Lightroom CC as part of the Creative Cloud Photography Plan - Creative Cloud pricing and membership plans | Adobe Creative Cloud