For painting- prime with oil primer. The paint can be oil based or acrylic depending on your preference. Varnish isn't needed, this is a clear coat not a paint.
It is important to use an oil base primer. This will stick better to old varnish. The finish paint can be any type. The Minwax is a clear finish and is applied over new wood stain only.
Do not apply polyurethane or water based clear finishes over varnish, they will have adhesion problems.
Restaining can be done over well prepared varnish but it is better to strip, sand and restain. It depends on the overall condition of the handrail. Chips and scratches will require excessive sanding which will remove the old stain, this will show in the final product if the entire handrail isn't also fully stripped and sanded.
Hope this helps!