The best way to develop your film chops is to pick out a few filmmakers and really watch and understand all of their films. Here are a couple of essentials you should check out:

Stanley Kubrick: every single one of his movies are great, although some are kinda inaccessible (i.e. acquired taste)

P.T. Anderson: Magnolia and Boogie Nights are probably both in my top ten of films, his other 3 films are very good as well, although they are slightly less accessible.

Coen Brothers: all of their movies are good, but they have a weird habit of cranking out a fucking amazing film (i.e. Fargo, No Country for Old Men), and then putting out a couple of clunkers in comparision before making their next absolute masterpiece.

Martin Scorsese: needs no description

Charlie Kaufman: he's a screenwriter, not a director. Adaptation is in my top 5 of movies probably. Eternal Sunshine and Being John Malkovich are also essential.