Individual Category Viewer With Wordpress?

I want to set up my site as an online mag. I want to display 12 different categories that show the image for the latest written article along with an excerpt of the article and then also display the last three or four articles written within that category...similar to this joomla page here:,6,7,8,9,10,11

The Only problem with this example is that it takes up too much space, so i would like to find another way to display the a self contained widget for each category that has a scroll bar or maybe a pop up.

Is this even possible? (I'm extra new at this so any insight would be a biiiig help) THANKS!