My favourite lighter style is a blue flame torch style lighter as these produce the hottest flame and don't go out in the wind. These are usually chonkiest and I don't carry one on me generally unless I'm going to have a cigar which is not very often. Usually I keep these lighters at home and use them to burn incense.
I do however always carry a small cheap yellow flamed lighter in case I have the pleasure of a Polish guy coming to ask for a light and I can get a 'thanks boss' from him. I used to have a plasma arc lighter which would impress everyone that I gave a light to but I lost it unfortunately.
I don't think many carry matchsticks anymore. I do quite like the striking of the match but generally don't need to use them.