As Kennen, I suggest being AP, try maxing out his skill shot and try practising harassment with that. Also his ult and his passive can make any situation good for your team but hold off on it when in a team fight cause usually people will switch their focus on to you as you rush in with that ult.
I usually get majei's or rylai's staff first depending on my game, then go for zhonya's. The Zhonya's allows you to semi-start team fights with your ult and then use the ability to be invincible for 2 secs.
Major problem with most Kennen players is to know when to use your skills and not.