Also, if the case is glossy, it may need just a light sanding to roughen the surface so the new paint will adhere and not start dripping or streaking.
I'll second this, not enough to go all the way through the factory paint but enough to roughen the surface to help the new paint stick, I probably wouldn't actually use sandpaper, my usual product of choice is "3M scotch-brite Maroon grade" because it's abrasive but not enough to leave you with deep scratches that show through the spray, If you can't get hold of that use the finest sandpaper you can get. After you've done this clean all the dust off with a damp cloth then leave to fully dry
If you take the above approach you can probably get away without primer (because the factory paint that you've now roughed up to a matt finish) is now acting as primer. To get an even color I would recommend doing at least three thin coats to avoid drips (as Ralston18 said), usually it says on the can to do them 15-20 minutes apart, depending on temperature, what your aiming for is to do the second/third coat when the layer of paint underneath is almost dry but very slightly tacky, you should be able to touch it without damaging the surface but it shouldn't feel fully hard
as for what kind of paint to use, any spray designed for use on metal will do, as a rule of thumb I never buy the cheapest brand, but the second cheapest is usually fine, the last paints I bought were Hycote and I got good results on metal with them
because pink is a tricky color to buy off the shelf, I would go to an automotive store that offer a color match service, where they would be able to mix a shade exactly the same as something you brought in, or from catalogues of thousands of shades from car manufacturers, allowing an almost infinite choice