Classicist here!

Athens' tendency to cremate their dead was rather unique at the time - other Greek states would simply bury their dead. I've read that cremation was somewhat associated with heroic status, but unfortunately don't have any evidence at hand to suggest that was the case.

The ancients were serious about looking after their dead. Athenian funereal rites took three days, female relatives were expected to make a show of mourning, it all ended in the ekphora, a pre-dawn procession to the grave site, and everyone had to purify themselves afterwards. Post-death tomb visitations were regular, and relatives were usually laid in the same burial grounds as one another to make visiting and performing customary rites a little easier. The design and appearance of the tombs did differ throughout the ages - I believe the rise of democracy in the 5th century made graves a little simpler, but in the 4th century became more extravagant again. In 317 BC Demetrius of Phaleron made it so that only the simplest grave-markers could be used, so as to stop unnecessary costs. But the stelai that have come down to us are incredible - some huge and majestic with depictions of gods and heroes, others that are simple heartfelt commemorations to loved ones.

The best case study for you would be the cemetery at Kerameikos, which was in use from around the 8th century BC through the Classical period. The link I've provided should show you a bunch of photos from the museum, where the original graves are now kept, but if you visit Athens the graveyard itself contains replicas of the most prominent! Also, if you can get hold of Robert Graves' The Greek Way of Death or Oakley's Picturing Death in Classical Athens, they would both be incredibly informative. From what I remember, Graves in particular talks about the cremation method at length. Hope this helps!