Filter by category and update URL
When setting up the category, you should be able to specify the URI Format which in your case would be "our-work/{slug}" then setting the template field to point where ever your category template is (You could point this at the same template as the overview and do a some checks but if you're beginner you'd probably better off having them in separate files).

Once you're loading in the new template, you need to get the projects that are related to the category by doing: 

{% set projects = craft.entries.section('projects').relatedTo(category).all() %}