picture-based theme

It’s so doable with WP.

Pick WP theme that has less style in it, base theme or blank theme, so that you can assign the style without much work on overriding stuff that already there.

On the menu part, depends on how you manage your content, for example if you use post and category or tag, just query posts based in category (or tag) and get only the feature images, make them clickable linked to that post.