Best way to stain my wooden stairs and handrail

[larry8]

I recently moved into a new house - it was built about 4 years ago. The wooden stairscase feels like it was never stained/varnished as it looks quite different to the floorboard which are darker and glossy. I was hoping someone could give me some tips about staining these stairs and handrail. I've watched some videos online and understand that I'll need to sand them down, prime and then apply a few coats of stain. Do you have any recommendations for this job and what product would be best to use? How can I make them nice and shiny/smooth at the end? Thanks very much for your help.