Installing 3/4" engineered hardwood on first floor. Starting off with new subfloor, was a gut job. My question is it has a open staircase to basement, somewhat like a Z shape (please see attached diagram). I was thinking of building the pieces for the bullnose, making sure they are square. The 1st board would attach to the bullnose on the first step, and I would square the room off of that. So I would be almost starting in the middle of the largest room.

Am I on the right track, or are there other ways of doing this. The hardwood will go into every room except bathroom and foyer.

Any help with this would be very appreciated. I can't figure out how to upload my diagram??

You are on the right track. Glue the first plank next to the nosing, and the nosing, if it isn't already fastened.