Karthus is a very strong pick right now with the current meta, as he has good poke in lane, great utility with his w, and an insane ultimate. So, lets move on to the build order.

In order to utilize the insanely low cd on Karthus's q, you should build a Lichbane as one of his core items. So the build order should go as follows: Doran's ring (two health pots as well), Stinger, Fiendish codex, Nashor's tooth, boots of speed, Sheen, Aether Wisp, Lich Bane, Guinou's Rageblade, Hextech Gunblade, Boots of Swiftness, and a Rabbadon's Deathcap.