I have been watching nothing but Godard films the past month, so I'd like to offer some recommendations. I would concentrate on his 1960 to 1967 output (15 movies). Breathless, My Life to Live, Band of Outsiders, Pierrot Le Fou, Alphaville, Weekend and Every Man For Himself are the best ones, in my opinion.
I haven't seen A Married Woman, Two or Three Things I Know About Her, or La Chinoise in many years, but I remember liking them, and I hope someone puts them out on DVD soon.
11 of his films are available on DVD: Breathless, Le Petit Soldat, Une Femme Est Une Femme, Vivre Sa Vie, Les Carabiniers, Le Mepris, Band A Part, Alphaville, Pierrot Le Fou, Prenom Carmen, Soigne Ta Droit.