when you are customizing one of the default themes like Twenty Twelve, strongly consider to create a child theme to work with; http://codex.wordpress.org/Child_Themes
you could create a page template: http://codex.wordpress.org/Pages#Creating_Your_Own_Page_Templates
and use a query to filter posts by category;
http://codex.wordpress.org/Class_Reference/WP_Query
you can find an example in my recent post.
Thank you, I will try all your suggestions.