The categories will work fine for you, but first a couple of points. The main page of the site will display all the posts from all categories in reverse chronological order (newest at top).
If you do not want to have a page where all of your posts are listed, you can set a static front page for your site. If you wish you can also have a "posts" page that will show all the posts. If you do not, simply do not create that "posts" page.
Next you will want to create a custom menu and in that custom menu include the categories that you desire along with any other items you wish (about page, etc.). If you click the "view all" link at the top of the pages module you will also see a "home" page tab. You can include that if you wish and it will link to the static front page you set for your site.
You cannot exclude posts by category on the normal main "posts" page (typically the front page of the site). It will always show all posts.