My two personal favorites:
Cisco IPTV
VBrick
VBrick is more of a converter; feed it video, it puts it on out over Ethernet to a client on the PCs. I believe that they now can also feed a TV (via composite or S-Vid) directly at the receive end. Of course, "live" can be a tape deck, camera, DVD, whatever. I like the VBrick, they keep it cheaper by allowing you to choose the level of encode by-the-box (one box does only MPEG1, one box does only MPEG2, one box does MPEG4 (very nicely), and they have models that do a mix, you get to choose.
www.vbrick.com
The Cisco IPTV is more of a encode / store / Video-on-demand (over Ethernet).... but it will also do live, and it has a hardware MPEG encoder that does a pretty good job. Pretty big bucks ... but since it's for a school, they won't mind burning another bushel of hard-earned taxpayer dollars so the chillen can watch "Scooby-Doo Does Addition (grade 12)" (j/k :-}).
The IPTV comes in several flavors: There's a "Starter Kit" (one box does everything) and there's also separate encode/broadcast, storage, and control units designed to cluster. They'll multicast or unicast, live or Video-on-Demand.
If you just want to pass video (and audio) over UTP/Cat5, then there are a number of BALUNs and adapters to do that. Check out a lucent (probably Avaya now) 380A adapter: it's composite video and two audio channels over UTP - The specs say it can do several THOUSAND feet over Cat5, and it will, with some loss of quality. IT'll do 100 Meters standing on it's head though - I use 'em at home - no noticeable degradation in the video.
Unicom has a (slightly) cheaper alternative, the model number is VAA-U501-VA. Same thing, composite video and two audio channels. Avaya and probably Unicom may have S-Vid units too.
I have and / or have used all of the above. It all works very well.
Good Luck
Scott