Our 18 yr old pool was remodeled a couple of months ago, new coping, tiles and plaster. I think the original coping is called flagstone or sandstone and it flakes too easy. Not a single flaw with the existing tiles but according to PB, it has to go when replastering. I would say, PB engaged professional subs and they completed the project in the order as PoolGate stated in his post....coping, tiles then plaster. We agreed to go with Quartzite coping although I'm not really sure if that is what we have installed now.
The stone varies in thickness when delivered but workers tried their best to match the stone in groups. The strategy is to break the big chunks and install them next to each other. Same thickness goes inside, thin or odd size outside. Coping sits on top of the wooden plank (waterline tiles width) to maintain level as shown in the pic. It was a laborious process and took 6 days for 3-4 workers to complete the coping. Hope this helps!
Here's how it look before:
Quartzite coping installation:

NPT GemStone Blue Tile/ InyoPools 12V LED's installed by your humble servant