I am loath to recommend themes, as there are so many good ones, and it most work fine with our plugin. You do not even need to find one that has Portfolio built in as a post type, as it is easy to add custom Post types and the custom taxonomies for those with plugins like Custom Post Type UI.

Our demo site uses the free Twenty Seventeen theme, for example. I would be inclined to use something like that to start with. Add the plugin I mentioned above and use that to make the Portfolio post type and a ‘category’ taxonomy for that called portfolio-category. I would then install the Post Grid plugin and our plugin, and set those up using this method:

https://searchandfilter.com/documentation/3rd-party/post-grid/

I wouldn’t be too concerned about style and appearance, and instead I would focus on function.

There are a lot of free plugins that will help you enhance a theme like Twenty Seventeen, and there are a lot of helpful free resources on ‘how to …’ for it on the Internet.