I need to develop a website and the website need to be responsive. I haven't developd a site since 2011. I always developed with 960px, but now I already did some Google search now and I view some statistics that say that nowadays the resolution most used is 1366x768. So maybe its better develop for 1366x768? Whats your opinion?
You can use StatCount to give you a idea how much market are you losing (the link points to screen resolution statistics for North America in the last year period).
First you can try to support all screen resolutions you can. Now, how much work do you need to add support for lower resolutions and how that ill affect your site? It depends a lot on what do you want and how do you develop your sites.
It's a trade off and only you can tell if you need to support that resolution or if it a waste of time and money.