The gloss level is of no consequence...get the gloss level that you think will look good with your existing floor and the stair railing. Some people consider their stairwork to be furniture and so they apply satin.

Find out what finishing product was used on the nearby floors, if they are unfinished on-site. If they are prefinished, then you will have to make a blind call on what to use.

I use commercial waterborne two-part wood floor finishes and know very little about the oilbase products, except to say that they take forever to cure and are prone to marring until that curing is complete.

Hopefully more folks will come in with their recommendations for you.

Whatever you chose to work with, test first to see if you will like the results and only work with products specifically rated for use on floors.

The commercial quality waterborne polyurethanes will give you the lightest results, if that is what you're after.