Krylon High Gloss Black Polyurethane Oil Enamel (KDQ6203).
It looks a lot like Japanese black lacquer, but is a lot more resistant to scratches and cleaning chemicals (and is a lot easier to apply, if you don't have spray equipment). I REALLY like its performance (application, leveling, etc.), and its surface hardness is very good, after about a month or two. I used it throughout the back part of my HT (countertops, refrigerator face, a large wall sconce, and these poster marquees). I usually get it at Wal-Mart.
I prime most MDF projects with Kilz (also available at Wal-Mart).
One note--- I didn't bother finish-painting the interior of my boxes (the face behind the poster)..... I was a little eager to get the boxes up on the walls, and I didn't want to worry about a poster sticking to a non-fully-hardened paint. So, Kilz primer is the only thing behind the posters.