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.
I strongly suggest you to don't use capacitor in this system, it's not AC and you don't need to compensate the coil reactive current.
Contrarily it creates problems, it creates a peak of current which may generate undesired spikes in the power line, it stress the driver with peak current, it slows the rise of voltage in reflecting to a weaker connection during the contacts approach. No one is using this condensers in DC systems