How do I create a view with some customization?
I wouldn't use Fields setting for this case.

Try to override template for specific content type and set your view to display your content type in specific 'view mode' for example teaser.

In your view change 'Format' to 'unformated list' and change 'Show' setting to 'teaser' for example. This will display your content type in specific view mode, so now you can override your template for this custom content type using:

node--my_content_type_machine_name--display_mode.html.twig

be aware of correctly using double dashes, otherwise your template won't be registered by drupal. Then you can code custom HTML template for your content type in this specific view mode and you can customize your layout according to your needs.