Out of the ones listed there, my fave comedy arcs are scandal, owee and omnyoji. Fave serious arcs are Shinsengumi Crisis, Yoshiwara in Flames, Red Spider, Four devas, Courtesan of a nation. Although mentioning them here isn't making any sense since you've yet to watch any of them lol
EITHER WAY, it is these serious arcs where Gintama truly shows it can do drama, action and comedy all simultaneously - and better than most of the great shows of those respective genres. :p