Ez can go mid situationally, and I like him most in that role because he benefits a lot from levels, both for the early ult and high levels of Q and E. He does a LOT of damage with his harass but is quite squishy. His real bane is people who can keep up with him and consistently disable him (especially heroes like Kassadin and Ahri).
He definitely should be building AD items, but his playstyle is much more like an AP nuker. He's on the weak end compared to some other AD heroes you could be playing in bot, so I wouldn't pick him for that role.
He can also jungle (lol), if you REALLY know what you're doing. His clear is actually quite safe and very fast, but he is a pretty poor ganker and needs too much farm for it to be really viable. You might as well jungle TF instead. :P