I can sort of meet some of your criteria.
1 mouse/keyboard used to control MULTIPLE computers, but only with MULTIPLE monitors.
(each computer would have a keyboard/mouse to boot properly, but wouldn't need to be used).
If multiple monitors is out of the question, you can get by with an arrangement of A/B type switches for all the computers to share I guess.
FREE should fit your budget.
I use a program called Synergy.
http://synergy2.sourceforge.net/
It operates over TCP/IP. It even works on some Linux/UNIX stations - including using the clipboard.