I'm confused as to which is the before and after. One has beautiful wood floors, and one has them removed, so I'm hoping the first picture is what has been done. Personally, I wouldn't paint them at all, but if you have to, you shouldn't paint them with anything flatter than satin finish because stairs tend to get dusty and should be easy to clean. I would try to remove the varnish as much as possible to get as smooth a surface as possible, but you're not likely completely remove the varnish and certainly not the stain, so don't expect a big colour change. Assuming the first picture is its current state, I'm assuming it will look like the picture below, which I think is a nice look.

The first photo is the before photo. We ripped out the laminate and we are installing natural hickory hardwood. The photos with the white box newells and white balusters are the current photos

To be honest, I think you've ruined the elegant staircase design with those chunky newel posts.
If painting, I would paint the risers white and stain the treads darker, like the photo thethistle has posted.

This staircase was my inspiration

I think I'd remove the trim and half newel post on the wall.

Scuff sand varnish use a quality oil primer and use a high quality paint fine paints of Europe has amazing paint I would use that if you are doing it yourself maybe use Benjamin Moore advance or satin impervo fine paints can be difficult to use. Paint the treads Newell's and skirt board white and paint railing different black grey or choose a color that matches some of the colors in your home .