How do you approach block structured content?

It really depends on your specific use case.

how you're structuring your data to begin with, how much content do you have for the site (is it 10 pages or hundreds?); will the same content or information be used in multiple places on the website, how do you plan to update it (are you expecting to integrate 3rd party APIs into it or just have end users manually update it?), or is very dynamic, like an e-commerce site? and what languages (PHP or JS) are you more comfortable with..

If you're looking to build something like the example that you provided, with maybe a dozen or 2 pages, less than 100 images) that won't be replaced very often, custom fields although extremely useful, are likely over-engineered for your use case.

If you're making a custom theme for someone as of now, you'll probably use a combination using blocks for the "post content" and then the traditional methods (the customizer, etc) and php templates for the layout (the heading, any sidebars, footers, etc).

Lastly, there is a big transition of how themes are being made in Gutenberg with the full-site editing initiative going on (and is not quite ready yet for the public), just keep that in the back of your mind, depending on how much on the 'cutting-edge' that you want to be and how much your comfort and experience with react and javascript is.

PS: For anyone reading this, the recommend advice here (July 2020) will be possibly outdated in just a few months depending on how the greater development and adaption of Gutenberg and full-site editing by the WordPress community.