Latex paint is the most common choice for painting MDF because it is easy to use and gives the wood a nice finish. Oil-based paints and lacquer-based paints are also options. These paints give a different finish quality than latex paint, and are easy to apply with a spray gun.
Always prime MDF with an oil-based primer/sealer before painting. Never use a water-based primer -- MDF absorbs water very easily, which creates a grainy surface texture that cannot be removed with sanding.
If the base has been primed/sealed, using a water-based paint also works because the primer seals the wood so it cannot absorb the water into its fibers.