The easiest way to update the railing is to just paint the spindles white. Leave the top rail natural wood. I have several pictures saved with metal spindles because we are changing a railing in our house. Ours was a dated builder special disaster so we have to replace all of it. So here are two options with metal spindles. Even though they are stairs the concept applies to a railing.

Staircase and Railings · More Info

Transitional Metal & Wood Staircase · More Info

I assume you mean the spindles not the railings per se

Painting them white

When I think of sunrooms, bright and light come to mind. I would paint the railings, spindles, window trim and baseboards white and place an area rug on your new wood floors.

IMO replacing the spindles is the only way to update them all the paint in the world will not change the fact they are dated . What style are the baseboards that might give me a better idea of the style you 're going for, Showing the LR might also be helpful questions with no context are difficult to answer.

Photos added. Thanks