Extinguishers come in different types, the most common of which are water, CO2, dry powder, and halon (or a derivate).
Water extinguishers are powered by compressed air or gas, and are normally larger than would be car-mounted.
Dry powder is an economical choice, but leaves LOTS of mess to clean up afterward.
CO2 is very effective and class B and C fires (flammable liquids, electrical), so it's apprpriate for automobile use. You need to get close to your work, i.e., 3-6 feet.
The best choice for effectiveness, ease of use, and minimal mess is a small halon extinguisher. Many owners mount them on the tunnel, forward of the shift lever. They're not cheap, but a smaller concentation of gas is effective at fire suppression.
Lots of car owners buy an extinguisher, mount it, and forget about it. When they try to use it, after they figure out how to release the extinguisher from the bracket, then release the trigger mechanism, they can't open the engine lid, because it's now REAL hot.
Does the phrase "Charlie Foxtrot" strike a familiar chord?
Everybody makes their own choice of what works best for them. Buy one, look at it once in a while, and inspect the pull-ring or release mechanism. I guarantee that you won't regret being slightly anal about your extinguisher if you ever really need to use it in a fire situation.