First clean up the banister and spindles - make sure they don't have any wax, etc.

I would remove the carpet, and fill the bad dings in the stair treads. Don't use too much filler - it will make more work to sand down. Use a plam sander with 80 grit to sand down the filler and lightly sand the bull nose of the stairs. Follow up with 120 grit sanding.

Vacuum everything and use a tack cloth, then stain the stair treads. Follow this with one coat of polyurathane. This first coat of poly will prevent any paint that might bleed from sinking into the raw wood.

I would then mask around the spindles and risers, and paint them two coats.

Finally, lighly hand sand the treads, vac and use a tack cloth, and give them 2 more coats of poly.