There are different ways you could do this. I’d say the easiest way would just be to use what’s already setup in WordPress; just link to your category archives. You can do this easily from the menu builder under Appearance > Menus.
There are several other ways you could display posts, as well. Checkout the “Redefining the Blog” video series in your documentation.
And additionally, under Appearance > Widget Areas, you can create custom widget areas and then apply them to specific pages, category archives, posts, etc. There’s also a video series on this subject in your documentation, as well.