Painted stair treads show wear very easily and can get slippery.
For a better understanding of your situation, pictures would help.
The subfloor is likely just plywood, so you'll need decent risers and treads that look nice and have a rounded edge. Its likely you'll have to remove the railing and all the spindles to install the treads, then reinstall. double check your rise at the top level and the first level as all risers should be equal distance. adding 3/4" will keep all of the risers the same but will change the rise of the first step and the last step in reference to the floors. While this doesn't seem like much, its a PITA and causes tripping and can injure someone. Its just bad practice. You'd have to adjust the stair stringers or fudge the differences to the point where all risers are the same so you don't have a 3/4" taller riser on the first step and a 3/4" shorter riser on the last step.
trim and moulding against the wall will need to be adjusted most likely as well. This may damage the wall a little, thus requiring some patch and paint work. Its relatively easy, but is additional work none the less...
