One question: does the center spindle (not sure what it's called but the one that's fatter than all the others in the middle of the swirl at the bottom of the steps) - does that get painted too or should it match the railing?

I have done this. We have oak railings in this house that were very ho-hum, so I decided to stain them darker with polyshades. I mixed Walnut & Bombay Mahogany & while I would have liked them to be a bit darker brown & less reddish, I'm very happy with the way they turned out. My railings did not have a really shiny finish, so I didn't sand or anything, just painted right over them with the Polyshades. I used a small cheap chipbrush, so I could just throw them away, since Polyshades is oil-based & I hate working with oil. It covered really well in one coat & I just went back & did a quick 2nd coat on areas that were a bit too light. I didn't even tape off the spindles or anything & it was quite easy to control the coverage. Here's a before & after..the best pics I have available right now. Now the railings are much darker than the floor & I think it looks much better & richer. And it really wasn't hard to do at all. Well worth the effort. Before: After:

When stain is applied correctly, it is absorbed into the grain of the wood. Woods with more dense grain(like maple) absorb less stain, so sanding is generally less time consuming. Wood can be stained darker, but not lighter. Stain will not be absorbed through any finish(save what is called a wash coat of shellac which is used to minimize blotching). Blotching occurs when a section of the wood absorbs more stain than surrounding areas because of the grain density. Softer woods(pine/etc) and open grain woods(oak/ash/etc) tend to blotch more than more dense grained wood. Sanding finish can be quite time consuming and expensive, especially when the old finish gums up the sand paper. Which happens more times than not as a rule. Scratch coat sanding is an exception, since the finish is not removed, but just roughed up so primer can adhere better.

Be sure to sell or give away that beautiful old railing and not throw it on a heap. I happen to like it. But indeed, it might look better in black. The railing you have posted instead gave me some shudders. Quite a contrary style and not one I'd welcome in my home. Way too modern for a ranch home, is what comes to my mind. If you are really going to get a new railing, I like the one Judy proposed, although I wouldn't want it in white at your place. Perhaps in black and the railing that matches the wood of the stairs? Or maybe something like this?