Video Streaming Help

Ok first let me start by saying this might not be in the right forum, but I thought this was the best fit for it.

I am helping my school try to start a broadcasting class. Several other schools have it, and they all accomplish it differently. I helped the middle school a little, and theirs works ok, but a lot of it is old PCs and just kind of "rednecked" together. The things I want to improve upon are:

A-the PC that does the video mixing (in conjuction with an actual video mixer, the PC is used to play back videos and add overlays/music/etc etc)

B-The streaming system

I've got an easy solution for problem A, I'm just going to help them pick a better PC to use (the one the middle school has is VERY underpowered, little Pentium Dual Core and a cheap GPU running 2 monitors and a video mixing program)

Problem B is where things get a little complicated. The schools have been using these little things called vBricks (evil little problem causing devices if you ask me, if I had a penny for every time we had an issue with that stupid thing I'd be a millionaire). To help with this, at the middle school, I talked them into letting me put Linux on an old laptop, and hook up a USB capture card to stream over uStream. That works great, except for the ads that show up on occasion, and the capture card was a little funky sometimes (driver support for Linux wasnt great).

So I am wondering if anyone knows a good way to do this for relatively cheap. The goals are:

Be able to stream live to the entire school, and preferably also stream to people outside the school's LAN. The vBrick had a number of issues, and we had to have the stream set to very low quality so that more than about 5 clients could connect. I read about multicast to eliminate this problem, but I have no way of testing it, and on the vBrick's screen it always said "Multicast mode enabled" so I'm not sure how they had that all set up...

Be able to essentially "DVR" the broadcasts so that teachers and anyone else who needs it can go to a page somewhere and view the broadcasts like "Video On Demand".

Be able to stay up 24/7 while being relatively easy to maintain

Be able to stay away from Windows (they'll let us be the admins of a Linux machine, which makes troubleshooting easy, but on a Windows machine, I've gotta go run and find a computer teacher every time I need to do something that needs elevation)

Be relatively inexpensive. The reason for this is because most of the time I'm the one who ends up maintaining this (moreso than the IT guys from the central office, they're usually a bit overworked and busy with other things) and I liked the Linux based streaming approach because I had control over it and could fix things easily. The vBrick was protected though, and I wasn't allowed to do anything besides turn it off and on, so for example one day when it had an IP addressing issue it was almost 4 hours before we could do anything about it. Plus this stupid vBrick costs several thousand dollars, and even a very nice PC costs less than that, so if there is a good way to do this with a PC then that's how I'd like to point them.

Can anyone suggest anything? I would like to use an internal capture card, but the video mixer they are planning to purchase is only standard definition so we don't need to blow $200 on an HDMI capture card. As far as the video streaming, I looked into FluMotion, but I don't think we can set up the networking to make it viewable outside the LAN, and it doesn't seem to have "DVR" ability like we need.

Can anybody shed some light on this? I'm only a teen so for large scale video distribution I'm a bit outside my comfort zone...