Well, the first thing I would do is look what you already have.
The PC with the CP hooked up to it will have a interface/encoder board of some kind.
It could be a Ipac, Could be a Xin mo, could even be a hacked keyboard you will need to find out what it is.
If you aint sure take pics.
The board will then be attatched to the PC, Is it PS2 or USB connection?
Is there any other hardware? Spinners, trackballs etc?
Most controller interface hardware on a pc is plug and play it gets recognised as keyboards or mice etc.
Tbh the hardware side of things is easy as long as the stuff you have is compatible with the new PC.
Now software is again easy in theory but can be more of a pain in the ass in practice.
You need to decide what emulators you will be running and look at their specific needs.
Some emus like mame are fully customisable for controls so are easy to set up.
However some games and emus are not so easy or customisable so its best to take them into account 1st and then work your control layout around them.
If you have a Ipac for instance this is not a problem as you can program the input to whatever you want on the fly very easily.
If you are using a xin mo this is not the case and more effort will be needed.
As for hyperspin that needs to be set up last once all your individual games and emus have been set up first.