What color(s) are in the rest of the home? BTW...I think it would look great to paint the lower wainscoting white. With your beautiful formal dining space, I think you need an equally beautiful chandelier. If you want to bump up the style, I think reupholstering the chairs in a pretty fabric would look quite nice.

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I believe that paint is the last thing you should do to your dining room. The place to start is with the chandelier. There is nothing as beautiful as a crystal chandelier, it alone makes or breaks a dining room. Expect to pay $900+ for and 24-26" wide crystal chandelier. Once you have your chandelier, it's time to look for art for those big blank walls. One large piece per end wall is my preference. Tapestries and Oriental screens are always elegant choices. Next, select a rug. It's hard to go wrong with a Persian rug whether it's antique, new or imitation. At this point, you will know what the colors for your room are and because you have selected things you love (never buy things you don't love), you will love the colors of your room. It's time to select draperies, new fabric for your chairs and determine if you need or want to paint.

Best of luck with your dining room.