fire extinguishers

Yes, you should absolutely have a fire extinguisher in your car (even if its not a classic!). And one in your garage, and one in your house (kitchen). Minimum. If you have a big shop or garage where you work on your car you should probably have a couple, especially if you do any welding. Just a good old ABC dry chem is all you need, that will take care of pretty much everything you encounter with your car or in the average garage.

Dry chem's are messy, but they're the only thing that will really work for this application. Halon, or halon substitutes now, or CO2 extinguishers are not really the right type for automotive use, they get used in tech industry more than anything. Rubber products retain heat and will reignite as soon as the halon substitute or CO2 clears. Fuel fires will have vapors present again immediately after being extinguished with an inert gas extinguisher, ready for re-ignition and even explosion. An ABC dry chem covers pretty much all the possible fire types for a car, and the dry chem smothering the area prevents re-ignition. Dry chem also works on liquid fires, like you would get with spilled fuel, because it will float on the fuel and prevent vapors from spreading again. Magnesium can be an issue, but for small fires a dry chem will work early on. Most fire departments don't even carry anything for magnesium unless there's a specific hazard like a manufacturing plant or the department as a hazmat team or crash/rescue rigs at an airport.

Car fires only take about 30 seconds to total a car depending on the source of the fire. A minute or less to a car being well involved depending on the source. No fire department will be there that fast unless your car catches on fire in front of the fire station. Yes, you have to use common sense, you're not going to put out a well involved car fire by yourself with a 2 lb extinguisher and you shouldn't risk your life trying. Or even a 10 lb extinguisher for that matter. But if you have a 2 lb extinguisher you can hit it when the fire is small, before it becomes a major life threat and before it requires really specialized techniques to fight. Even if you have a small dry chem and it doesn't completely extinguish the fire knocking it down will buy time for the fire department to get there, keeping it smaller longer. If you can attend a local class on how to use a fire extinguisher, even better. But really, it's not that hard. Yes, training will make you more efficient and mean you can extinguish more fire for a given size extinguisher, but don't use that as a reason not to have one at all. Something is better than nothing at all. And it beats the crap out of watching a small fire turn into a fully involved car fire before the fire engines get there, because for any significant source that's exactly what will happen.