Category Gallery -Portfolio

Hi, I’m making a theme from scracth and trying to achieve something like this:
https://demo.authenticthemes.com/board/

The portfolio-page is the index and has a gallery of all posts in the category “portfolio”(separating it from posts meant for the blog-page) and with an option of sorting by it’s undercategories in example over “Characters”, “Poster”, “Scenic” and ofc “Show all”. On hover captions show up with title, short summary and “see more” option. Clicking on the images in the gallery takes you to the post.

I’ve been googling but there is just too many different opinions, widgets and options.
Any suggestions on the easiest and most practical way to do this?

Kind regards
Susan