You'll need a stair nosing for the top step. For floors that
run off a stairway I always try to start there it is as the most visual part of the layout and you want it to look right. You need to see how square all the rooms are from the top step before you start. Don't confuse this with how square each individual room is.
Depending on the direction, the best way to find the squareness is by using control lines. In my drawing addition I measured out from both sides of the top of the stair. By doing so you create points of reference (blue) by using a chalk line. For bedroom #1 transfer the points through the doorway and snap another chalk line. Using the control lines measure against each wall looking for differences. A minor adjustment may have to be made with the starting stair nosing for everything to fall into place.
If the floor is running perpendicular to the top step....let us know.
By the way, the control lines are kept when the installation begins. You may want to check the differences after every six boards or so for squareness against the lines.