Also agreed about the target market: you're right in that the crowd wanting low-cost Ubuntu machines are likely to build it themselves.
As for a high-end Ubuntu machine: well, we don't think there is a need for us to do this. System76 and other vendors already do a good job with the high-end Ubuntu market.
School computer? Seems to me that a portable is preferable.
Office computer? Maybe - but not many offices use linux.
Libraries? This seems like a reasonable market to pursue.
Government Offices? Also might be reasonable. Big cost saver if the applications necessary are pre-vetted.
Maybe it would be worth talking to some local libraries or similar to see if they'd be willing to be a test bed for the machines.
Get Steam on there, and you could use them for video games as well, which is something libraries are now becoming open to in the interest of community building and getting kids in the building.