Papers every complexity theorist should read
Ryan William's Non-uniform ACC Circuit Lower Bounds and all the results cited therein. 

Not only is this a recent important result, it is a very well-written paper. Furthermore, the results the paper uses and cites cover a pretty good range of seminal complexity results. So if you trace through the references and read those as well - get to a point where you understand every part of the ACC lower bound from first principles - I would think that would be an excellent start to a graduate complexity education.