I'ved mained Evelynn for over a year and a half. That said, I don't often build her AP. Even when she was OP as AP.
Though, if I do build her AP I will generally go Deathcap first, she needs the damage. From there I will usually grab a Lichbane, then build situationally. With a DC/Lichbane she does plenty of damage. I try and build as much Armor/MR items as I can because it twofolds with her ultimate's shield. In fact, After I get Dc/Lichbane I will sometimes just build a GA right there. If not, I'll build a Gunblade, then GA.
That said, I usually jungle/top Eve so I'm probably not the best to tell you. I don't like her in mid because he laning is mediocre at best, and even with a good game you are unlikely to deny mid farm. I have better mids, though I do go Eve there once in a while for a change of pace.
Edit: I've never built a Deathfire's grasp, despite the awesome active I feel like it doesn't provide sustained damage and that annoys me. Also why I don't like AP Eve as much :P AD just provides more sustained damage and faster burst.