When to use different fire suppression systems?
I would say that your best bet is to go to a fire protection contractor and get their expertise, but I can give you a quick overview.
Your system is comprised of a sensor, your pipes, and the type of sprinkler head you choose.

Sensor: at what stage of the fire do you want to douse it? In order from early to later detection: Incipient phase uses an ionizing detector. The smoldering phase, where smoke particles are visible, uses a photoelectric detector. The flame phase uses a UV or IR radiation detector. The heat phase uses a fusible sprinkler head that is set to activate the heads at a certain temperature above the ambient room temp. My house has a sprinkler system that uses fusible heads. 

The pipes can either be a wet or a dry system. Basically, wet means you have water in the pipes, ready to go on signal. Good: quick when you need it. Bad, need a propylene glycol mix if you are in a zone that freezes (my garage, for instance). A dry system has empty pipes, which can either get filed by the fire department running water into the system or by a preaction system, where the water is stored in a tank, the detector sends a signal that the pipes should fill, then the individual sprinkler heads open up when needed in that section. 

The sprinkler heads can be crafted to your situation. Like I mentioned before, you could have the fusible head run the show. You can also have a mist head, which will leave less water damage. A deluge system has open heads on dry pipes, which can flood the area if needed.

Now this all presupposes that water is what you want. I don't know what you are burning, but there are four classes of fires to fight: A is ordinary combustibles, B is flammable liquids and gasses, C is electrical and D is metals. For a burning liquid fire, for example, you certainly don't want water, you want those heads to release a foam to effectively smother the fire. CO2 would cool the flame, but that would cause problems if you were stuck in there, too. 

Whatever has the potential to burn requires the triangle of oxygen, heat, and fuel. Remove one of those, and you have no more fire.

For your problem of the kiln, I guess I am having trouble picturing it. It seems like a lot of money and trouble to install a fire suppression system if it is a small pottery kiln. For a more industrial kiln, I don't know...Perhaps talk to the kiln's manufacturer and ask what their clients typically do for fire protection. I don't want to lead you on the path of something expensive and unnecessary. Good luck!