I am a former tech coordinator for a public school district. One of my last projects before I left was to develop a district-wide communication upgrade plan. Unless you have a lot of time on your hands and/or have a local vendor who can support it an Asterix-based solution is probably not a good idea. There are a lot of vendors out there that are experimenting with it, but I have yet to see one that has a solution I would call "fully baked". Whatever you go with, a proven track record and a local vendor who is certified to support your gear (and also has a good track record) is paramount. Nothing will make you look worse than a phone system that is a pain to use or is flaky. People have very high expectations when it comes to the behavior of phones, and absolutely will not tolerate the kind of BS they up with from their computers.- A Cisco system or Shortel system -- Education budgets vary wildly from year to year and reoccurring cost have to be kept down.
I find it laughable that you mention keeping costs down and Cisco or Shoretel in the same sentence. I have a Shoretel system in my office at my current employer, and it's very nice. However, it is also very expensive, and it's less costly than than Cisco... You are factoring in handset costs and extension licensing when you look at the cost of the system, right? Right? You are, right?
The best solution I found (and the one I recommended before I left) is the Rauland Telecenter VI. It gives great bang for the buck and is a highly integrated complete comm system designed for schools, so if you have bell, intercom, and clock systems that need to be upgraded as well, you get to do that nearly for free. It also lets you use Voip phones where you need big feature sets and $10 analog phones where you need "just a phone". Handsets are where a huge portion of the expense of a big phone system deployment go, after all. There also is no per-handset licensing, if I remember correctly. http://www.rauland.com/education/tc6/tc6_home.htm