Hi,
That shouldn't be too difficult.
You'll want to edit the file "listing_img_title" of the view "product" via the menu Display>Views. There, you can move around the different blocks and add additional PHP code based on what you want to display.
If you want to add an extra field to store the short description of the product, you can create a custom field of the table "product" via the menu Display>Custom fields (Essential or Business edition required).
Then, in your view file override, you can simply add such code:
<?php echo $this->row->XXX; ?>
where XXX is the column name of your custom field, and you'll get displayed the text you entered in that custom field in each product.