Finishing split level stairs

[Karen O.]

In my project, the stairs leading up are in good shape but require refinishing.  The risers & treads were painted beige and black (down the center). They appear to be oak hardwood.

The stairs to the lower level had to be rebuilt (didn't meet code).  They are new unfinished oak hardwood.

I know I'm painting the risers white.   But I've gone back and forth on what to do about the treads. 

Either strip the upper treads then stain/poly both sets or prime/paint both sets black.  

I don't think I can go wrong with either but wonder if I might be missing something like the amount of work involved.

The only other wood trim in the house are wood stair bannisters with a clear coat of poly. Everything else is painted white.

How would you finish/refinish the treads?

Thanks for your thoughts.