Hi, I have been a designer for 30+ years. I definitely would not paint any kind of stone, it will not stand up well as the paint will chip especially since countertops take a beating in any kitchen! Plus you will take away the beauty of the stone and it's veining for a flat uninteresting color that definitely won't last.

I would recommend you have the travertine polished, cleaned and then sealed, which you should do annually, especially with a stone like travertine which we never specify for countertops because it doesn't have certain properties that other stones and surfaces available today, which wear much better on kitchen countertops. I'm only guessing, but was the travertine countertop already in the existing kitchen? I see you selected a backsplash tile, that sort of matches the travertine countertop?

My suggestion, would do what I suggested above with the Travertine , don't paint it! Get yourself some undercounter LED strip task lighting and run it along the front lip of the cabinets on all upper cabinets. Also. add some recessed ceiling lights also LED available in round or square. It seems to me that the kitchen looks and feels dark and the lights with definitely brighten everything up and I know you will like it much better! Hope this helps?

If you're in a painting kind of mood, I think the cabinets are whats wrong not the backsplash. Black cabinets or a dark blue would go real well with the countertop/backsplash.