Welcome to the forums
Firstly, how does this "AEM EMS" thing work? How does it interface to the computer? Is it serial, usb, parallel, some proprietry interface? That will partly decide which computer to get.
Those screens look good. Do a search here for Lilliput for some info on it.
For computer, most here are going with the Via Epia platform, the majority now the M-10000 or MII-10000. These have 1GHz Epia CPU (about equivelent of an 800MHz P3), onboard graphics and sound, USB2, firewire, and the MII have a compact flash and a PCMCIA (laptop style) slot. They also have a single PCI slot.
For power supply, you will find, in all honesty, there is only one solution. Opus
For CDROM/DVDROM, take a look for a slimline USB2/Firewire one.
For kb/mouse, some people are using the Gyration kb/mouse combo. The keyboard is small, and the mouse can be used anywhere, even in mid air Make sure you get RF stuff, not IR.
The screen will come with it's own wires to connect to the blue VGA port on the PC. For connecting the PC to the amps, you will need standard 3.5mm jack to RCA cables.
For more information, pick out some of the product names in my post and go on a
In all honesty, you will probably find yourself needing to search for at least a week solid to find all the information you want