Yeah definitely. I'm going on a New Wave kick recently, I've got some films ready to watch in the next week actually. These are on my list along with most of Melville's work...
Two Or Three Things I Know About Her
Pierrot Le Fou
Vivre Sa Vie
I know there's tons more, but I'm trying to get the more well known stuff watched first, would you say that's a good selection? I went off of his top rated movies from Rotten Tomatoes, figured that'd be the easiest way to get started with his stuff.
Yeah that is a pretty good list, almost all of them are from the 60's period. But Le Mepris and Contempt are the same movie, Contempt is the american translation for the title.
From the list i will say the more well known are the last four, Contempt and Alphaville are also the most narrative and easy to go, Pierrot and Vivre Sa Vie are more tricky and full of the classic break of the cinematics rules from Godard, in fact, Pierrot was make without a fucking script and just improvising. Even then, Pierrot is my favourite movie in the world with Vertigo and i don't have seen another movie so great in terms of the relations between women and men.
Week-End and Two Or Three Things are more radical because they are related with the political things that has been hapening in France at the moment (may 68 and all of that) and with the gradually lost of faith from Godard in the cinema world and the scene. All the things he made post-67 are controversial because the people seems to think that him Begans to make cinema just for himself or for intelectual acclaim, i don't agree with this but you can judge for yourself.
Numero Deux is a strange experiment, is the first movie Godard makes in Video (and all his 80's work is in this format) and after 10 years without working a film for himdself. I think that in this terms is an important movie if you became a Godard fan or a cinephile and can support this kind of thing, if not you are good without seen it.
Also if you are in a New Wave roll, you should see some Truffaut, Resnais, Varda and specially Marker and Rohmer work (RIP). La Jetee was the inspiration for 12 Monkeys and is a just a 20 minutes film.