Pretty!! Think about logistics of cleaning at counter level too, especially behind the stove area. These types of embellishments are often used in a linear bar or a featured framed out area (or focal point) above a sink or cooktop. Be sure to weigh the esthetics to the clean-ability.
Is this metal or the nail on faux kind? From your post it sounds like it's installed already which would make spraying very difficult. Either way you can use CeCe Caldwell's Paint and Satin Finish. You can paint anything with this stuff. Really anything, glass, leather, fabric, walls, metal, plastic, laminate....you name it. And a little goes a long way! I use it for furniture all the time - www.shabbydaze.com
I would visit HomeDepot or Lowes and look at their spray paint section. I'm sure Krylon or Rustoleum has a spray paint for plastic, they definitely have paint for metal.
Yes, a good alkyd primer like XIM or Styx is where to start. If it was any place but a backsplash, any primer would do. But in this case, you will need maximum adhesion and durability. Be sure to sand it lightly before you start. . . just enough to rough it up and get the shine off.
Clean it with denatured alcohol and scuff it with a sanding sponge.
Then you can prime it and paint it.
The primer is the most important part.
Is it metal?
CP
Spray would infiltrate the whole kitchen +.
All you really need is a small foam core roller.
http://acpideas.com/index.cfm?XlinkID=12