Fortunately, PLA accepts many types of paints, most common of them is acrylic paint.
Acrylic is water-soluble until it dries, then it becomes water-resistant.
Depending on the goal you plan to achieve, different types of paints can be used - oil paint, already mentioned acrylic, enamels or lacquers.
Keeping in mind that manufacturers may present different types of plastic under the same 'PLA' brand, it is always good idea to try selected type of paint on a print sample to ensure that it sticks well enough and not melts the print too much at the same time.