Hi there,
My advice would be an AFFF (foam) extinguisher, followed by a dry powder.
An AFFF can be used on all 'common' domestic fires, even electrical.
I would recommend a small 2 or 3 litre one, if one extinguisher of that size is not able to extinguish your fire then I would suggest that it was time you left it alone.
My personal problem with powder is that it suffers from caking after a prolonged period of time. As the chances are that you would not be having fires on a regular basis my worry would be that a false sense of security would prevail in the knowledge that you owned an extinguisher that was possibly not of any practical use.
Having said that all extinguishers need to be examined periodically and replaced when the recommended shelf life has passed.
I would not recommend water or CO2 in the domestic environment but obviously if that was all you had then it would be better than nothing in the right situation.
Another problem I have with domestic equipment is that some people would feel confident that they had extinguished the fire and not call the Fire Service.
The best thing you can do is get smoke alarms, shut your doors at night, and take a mobile to bed with you.
IMO of course.