A short starter is a must, even with a coned muzzle. It is light and small, does the job, and unlike those things with the big wooden ball, it does not get in the way. Many people, in my opinion, carry starters which are too long and cumbersome. The next item is a breech-plug face scraper. I carry it because I don't know what else to do with it.
Some folks swear by plug scrapers.
I loan it out on occasion but have not needed to use it. To the left of the scraper is a ball puller. I carry it as defense against my own stupidity. A ball puller is needed only if you dry ball on top of a breech full of oil. Then comes the patch worm.