are you building these stairs up from "naked" stringers or is this a "skin" being applied.

Normal stair construction begins at the bottom...with a tread then a riser is set on that then the next tread up is installed...it is a overlapping type of method similar to shingles on a roof.

Paint first, then stain. Then you can touch up the paint once done.

after then touch up

sider stringers should go in first...then work you way up from the bottom Alternating risers and treads. You can "pre-stain" + varnish (poly) the treads ahead of time to eliminate some of the stain "bleed through" that often happens when taping off the white.