SqueakyClean
I believe most people are juicing their oranges with a citrus juicer (which is different from a centrifugal or masticating juicer), where you cut the orange in half and then twist it against the juicer (or if it's electric, you hold it while the juicer spins). MH mentioned that he had a restaurant-style juicer which is a press I think?
Anyway I think most people are NOT juicing the skins.
That said, if you want to juice the entire orange including the peels in your juicer, make sure the oranges are organic. You don't want to juice and drink all of the pestices, sprays, gasses and waxes they put on the regular oranges. The regular oranges should be okay without the peel, though, since the peel is thick. MH says organic is not necessary (but I don't think he juices the peel, either).