Two categories should do the trick.
- Featured posts – This category should be applied to posts that you want to show on your home page, with that images grid. You can limit the number of posts (so only the, for example, 6 newest ones would appear) and select the featured image for them on each post’s properties. You can limit number of posts easily, and you can also exclude other categories from your home page.
- Blog posts – a general category with a name such as ‘blog’ would include every other post you’ve got on your website. This category would have a visible link on your home page, and would be accesible through www.yousite.com/blog/
I think this would be my way to go.