how to load gallery form post via ajax

I would like to create one picture gallery in WordPress and will like to have category and subcategory. For e.g. Galley Sub Gallery Sub Gallery Sub Gallery Sub Gallery Sub Gallery Sub Gallery I want to create each gallery as a post so that In that particular post, I would be able to add a gallery and other content.

For the front and gallery page, I would like to show only sub gallery thumbnail (Say like the Featured Image), When you click on thumbnail, the popup window will appear (any kind of model box). Inside that, it will only show the gallery image with the “next” and “previous” option (Slideshow, next, previous, close button will be great). Maybe some model box script will have this type of option.

To understand what I am trying to say, I have attached an image mockup.

I understand it needs to be called a post gallery via ajex. If I can do all via ajex, then will be nice.

i like to do without plugins but if have any plugins then also fine.