Organising posts landing page

Hello everybody. I’ve pretty much figured out many basic and medium wordpress things, but I’m having a problem with organising pages where my posts land. To be precise, I’ve linked some of categories to my pages, and when I write a new post it goes under desired category. What I would like is to have control over those posts in that certain category page, I would like to organise them in tiles with thumbnail picture and short text, and when viewer clicks on that tile it will lead him to full post. But at the moment, all I’m getting is posts being showed in a hieararchy, and everything I can control is whether I want full width page without those default templates with recents posts and etc at right side, or not. So , could anyone help me ?