What is the best SEO app or plugin for a Shopify store?

Kudobuzz SEO is great for this and it's free to install. The app gives you two options, being that you can fix your SEO yourself or you can get the pro version which does everything automatically.

In my opinion, an app only goes so far with SEO. It's much better to hire an expert who can analyze on and off-page SEO and develop real strategies based on your content and needs.

Yoast SEO only identifies the areas that need optimizing, but you still have to edit the pages manually. Most SEO apps only provide a guideline, but you still have to manually optimize the content. 

SEO apps can help you to identify issues, but you or an expert will need to make the changes to the website. SEO also takes time and patience.