MDF, being a man made product has a uniform density and porosity. It is smooth and an excellent surface to paint.
That said, you will definitely need to prime the surface. I would give it one coat of alkyd or oil based primer, then sand it and give it another coat. After the primer has cured, lightly sand and apply two or three coats of automotive paint. For this you want to apply it within the specified so the paint isn't dry yet and the coats have a mechanical and chemical bond. After the paint is dry, scuff the surface and follow with at least two coats of clear coat. Color sand after the clear is cured, then buff with a quality wax. (Or follow the manufacturer's directions exactly on how and when to apply the paint/clear.)
That is a hell of a lot of work, but if you want the finish you described, and want it to last, there really isn't any other way to do it. As the saying goes, preparation is everything and if you half ass that, your finish job will look like shit.
Automotive paint is actually some of the toughest paint out there. As long as it isn't abused it will last a long time and still look great. Use PPG or DuPont.