I'm sorry no one has replied to you, I would have thought people would have jumped on this a lot quicker! I can only get a short response now (probably not everything you were looking for), but to be honest I think a decent normal computer build (somewhat specialized) would suite your needs.
IE. A multicore processor and a TON of ram.
Id personally suggest an AMD Quadcore or hexacore processor(or an intel i7 if you really want to shell out and get 8 threads), a Micro or full ATX board (so you get a good amount of sata ports for hard drives for storage), maybe 16GB of ram (only around $100 nowadays!).
It submitted before I finished typing haha, but basically you want a lot of cores/threads so the different machines can work without waiting for processor time and you want a lot of ram so that you can have a decent amount of machines running, each with at least 1-2GB of ram to make it realistic.
I would also suggest an ssd to help make everything run much faster. DO YOUR RESEARCH THOUGH! Not all SSDs are created equal. However, even "the worst" ssd (in terms of performance, not quality) is 80% faster than a HDD (due to seek times being almost nothing).
So I guess if you wanted a build
A decent motherboard (Gigabyte AM3 or AM3+): $90-115
A Quadcore/Hexacore processor: $100-150
16GB of ram: $100
A decent case: $50
Power Supply (Id go with the Antec 80+ bronze 380W one, it honestly is enough to meet all of that hardware. With my mb, quadcore, and harddrives I only run at around 60 watts idle 150w at most, so I think at 380 for this build youd be good): $40
---Id go with an 80+ bronze power supply or better since these tend to be on a long time, and why not get the same power and pay less in electricity
A decent SSD for 60GB: $100
Hard Drive (2TB would be a lot of space): $75
That puts you at $555-615 total (I did the math ), so below your budget. XenDesktop is free so no cost there.
And after youre done that could end up being a pretty nice HTPC, server, personal computer, etc! Let me know if you have questions or comments or want specific links to parts!