How to start establishing a yard lawn after heavy grading? ?

I had a large hill going across my lawn and I had a contractor remove about 350 yards of dirt. They graded and spread what was left to create somewhat of a flat yard. The ground is now as hard as cement i assume from compaction of the hill. The contractor mentioned I need to Lime the "he'll" out of it. I live in Charlotte, NC and summers are 90 degrees plus. I plan to seed in the fall. Will a core aerator penetrate such hard soil? Whats the most rugged grass available to grow in these soil conditions? Any advice on how to start growing my lawn the right way given the mix of fill dirt/ bull tallow/ red clay? I'm on a budget since the dirt removal nearly wiped me clean. Much appreciated.