Although usually Darius is an AD I'll explain why AP is better. If you upgrade his ability power first it actually ends up increasing the damage 40% for each 10 ap points, but only 10% for each damage point. Don't believe it works check out my profile stanfordl. If you follow this guide you will get pentakills all day.

If you don't buy them you will run out of mana too quickly and your Ability power and spellvamp spells will be useless. Also you need smite to one hit kill the wolves otherwise they will kill your turrets. And without clarity the minions will run out of mana.

I know people usually get q first for harassing, but harassing is stupid and only noobs do it. You need to go for the kill right away so drag em into the forest and have your entire team DESTROY him. Don't kill the minions just go for the champions.