The machine looks good.

2 axes of motion, plus a motor driving the tyre.
For linear guides you could probably look up the IGUS linear guides. Cheap, and drylin W especially has little play with the low forces you'll be using to cut.
Drylin N http://www.igus.co.uk/wpck/default.aspx?pagenr=1969
Drylin W http://www.igus.co.uk/wpck/default.aspx?pagenr=1994

The more interesting part of the project is the need for the machines to be operated by unskilled people (by that I mean people that didn't build the machine). A PC running mach3 is unlikely to be robust enough.

You'll need:
1) Safety (guards, big red e-stop buttons, etc)
2) A black box to store the program, give step and direction commands to the motor drives, and interpret operator button pushes (go, stop, jog cutter, etc).
3) Some drives to drive the motors.
4) Motors (probably steppers).
5) Power supply.

1) You can do.
2) This is the most interesting bit.
A Siemens LOGO PLC is too simple (slow) for your needs.
http://www.automation.siemens.com/mc...s/Default.aspx
But this Galil PLC may be over spec (still only 300USD tho)
http://www.galilmc.com/products/rio-47xxx.php
You can find a PLC somewhere between the two. The main constraints are probably the amount of I/O (for buttons, etc), and the need to find one fast enough to send step pulses for the motor drives.
3) Easy once you know what motor sizes you need.
4) Easy once you have an idea of the cutting forces involved.
5) Easy once you know what boxes you've bought to do all the above.

Hope it helps. Basically you need a PLC. lol Give me a shout if you need a hand getting something up and running.