For your room the first question which has to be asked is whether or not you are cabling through a plenum space as that will impact whatever cabling ends up being run.
We have regularly used 50' HDMI cables from Cables2Go which are plenum rated and work just fine. There are also HDMI stabilizers which help ensure that there are no issues.
For HD-Base-T, Aurora Multimedia has units which are powered at one end only and the other end doesn't require power, which is nice. Their HD-Base-T units are a medium build quality which means they are excellent for schools, but would not be recommended for true mission critical stuff. A higher quality unit might be found in products from PureLink which use a proprietary HDMI over single Cat extension that work phenomenally well and are dead on reliable in my experience.
Still, I find that HDMI at 50' is extremely reliable and is a good first choice due to price. If you are running through a plenum space you must get a plenum cable like this one...
If you are not running through a plenum space, then this should work just fine...
But, then if you want a HD-Base-T solution, something from Aurora Multimedia may be what you want...
Right on the main page of their site right now they are showing the HDMI & VGA combination model which accepts HDMI, VGA, component video, s-video, or composite video and converts it all to a single HD-Base-T cat-5e/6 wire and then HDMI into the display. So, you get rid of any need to switch inputs with that solution.
If the school is spending a bit to update things, they should go ahead and adjust the programming for a few hundred bucks or try to get it into the budget to take care of later... I know, good luck with that. If someone is up for doing it on their own, PM me.