I would paint it with a semi-gloss latex. This will have the best chance of dealing with the UV and heat exposure from direct sun. A light color will also help, last longer and keep the door a bit cooler.
Of course it depends on the look you want. Stain and varnish will look good but will require the most maintenance, you could be refinishing every couple of years. While a good paint, make sure to prime first, will need a little work every few years or so.