All of these things require some of the tradeoffs you suggest. I think the best plug in for photo displays, galleries, and descriptions/captions is the plug in I make glightbox. You could make Albums each as a photo post, it’ll automatically collect all of the photos in a single post into a gallery (or for multi-gallery posts, you can by hand name the gallery), and you can add captions and titles as well with styling.
To collect the posts, you can do a bunch of things, but I tag my posts into a category by searching for .jpg or .jpeg in the post content, as one way that I think is better than emoji-based tagging. You could then make a special index page that’s custom for those posts (showing all content paginated like a normal index page or something else).
To just get click to full size, you can simply use the Markdown photo syntax (![]() with the image in the () and alt text in []), but for captions and titles, I strongly recommend using the shortcode directly.
I don’t think you’ll get a much easier method, honestly. It’s what I built the plug in for, even though I don’t do a special photos page really right now (but I do special custom pages for my Books for example and my Now page. Here’s a description on building that custom page. My example for my letters page shows how to do a different index style page based on post category.