I refer to the diagram from this thread: What is the use of the capacitor in this relay circuit?, which is also shown below. If I were to use a capacitor for my relay coil (12v latching type) which already has a flyback diode installed, what voltage rating, capacitance and type (e.g. electrolytic, ceramic) should I be looking at? Also, if I were to use multiple capacitors for my set-up, would combining different types of capacitors be ok (e.g. electrolytic, ceramic), or not recommended?
Paralleling the coil with a capacitor can work the driver quite a bit harder (possibly causing it to fail) and may cause a brief dip in the 24V supply- which could cause glitches. If the driver is relatively slow or the current is limited it may be useful to reduce EMI from the coil, however the contacts usually dominate the noise and in any case the driver circuit will likely determine how big you can safely make the capacitor.
Chances are a reasonable value would be some nF and best served by a ceramic capacitor of adequate voltage rating.
Most people don't use one.
the Diode is going to catch most of the energy when the relay switches off, so the capacitor is only needed for the short period before the diode starts conducting, if that's a problem, use a slower switch.
The capacitor is not needed. The diode may also not be needed even if the relay did not have one. The drivers I've used in the past had the diode built in. See ULN5801 etc.