1. Standard USB A-to-B cable between the PC and the PMX-424
2. Stepper motor drivers, one for each motor. These translate the step and direction signals from the PMDX-424 to drive the motor windings. Depending on your budget and the size of your motors (dictated by the size of your machine), these can be some of the Geckdrive drivers. Or there are many other brands of stepper drivers, and even more Chinese clones of those stepper drivers.
3. A power supply for your stepper motors. Generally you want a linear power supply as opposed to a switching supply. You can by a complete power supply, or buy parts and put one together yourself. If the DIY avenue sounds interesting, look a the PMX-137 or PMDX-136. You will need to buy your own transformer (they give you links to a few) and a power switch.
4. Wire for step/direction signals. This can be pretty much any gauge of wire as it doesn't carry a lot of current. 22, 24 or 28 gauge works well.
5. Wire for the stepper motors. This may need to be a bit heavier gauge than the step/dir wiring, but that depends on what maximum current you are driving the motors with. I don't recall the gauge vs. current capacity chart off the top of my head, but a quick search should find one for you.
6. Wire for the AC power into the PMX-424 (lamp zip cord works just fine).
7. Limit and/or home switches - optional, at least for initial setup and testing. Typically mechanical switches, or optical sensor or proximity switches. Again, depends on your machine.
8. Something to mount your system on or in. The stepper drivers will need some kind of heat sink, and it it nice to have everything, including the PMX-424, bolted down to something. Some people mount them on a (fairly) heavy aluminum plate. Some people put heat sinks on drivers. Some people put everything in a NEMA enclosure and use the walls of the enclosure as the heat sink. Some also add a fan, and some do not. Again, this depends on what drivers you are using and how much current you drive the motors with.
That should get you started.