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There are thousands of sub-par SEO tools out there, which probably makes SEO tools the most convoluted category of them all. For that reason, my first recommendation for finding a great solution is looking for something that is clearly being actively worked on by developers. Many SEO tools were created quickly and are poorly maintained, avoid those. And some even slow down page speed load time- which is BAD for SEO, how ironic.
SEO apps are always going to be an important part of the Ecommerce tech tool stack. You need to be paying attention to how your pages rank in Google, and what those listings look like. You are especially going to benefit from SEO apps at a few key points of scale: starting, 10k visitors/month, 50k visitors/month, 100k visitors/month, and 500k visitors/month. At each point of scale, you will find yourself with enough budget to warrant a decent investment into a new SEO app or consultatative service.
Once you hit 50k visitors a month, you may find it worth it to do a $1k-$5k SEO overhaul, and maybe invest in a tool like Edgemesh. When you hit 100k visitors a month, you may consider investing in a headless commerce platform like Nacelle or Shogun FrontEnd, and maybe even your own mobile app, which isn't necessarily an SEO tool but it does improve the load time experience of your existing customers.
After 100k visitors a month, you have to continuously be investing in SEO and improving page speed load time as well as looking at technical ranking factors and working to improve them.
SEO apps are managed by the marketing team, and sometimes the developer team. Some of the tools are "set and forget" but most require frequent check ins to understand what is working, and what isn't, and you as the "head of SEO" need to be continuously improving your strategy, tackling new keywords, changing existing product details and descriptions to match trends and consumer behavior, etc.
You are of course looking for tools that can help you rank better, get more "free" traffic, and take a user from the journey of searching for a keyword, to discovering your brand, and then buying from you. That means these tools should understand your rankings in the SERPs. They should understand good title and meta description field lengths, keyword usage, and strategy. And they should help you make better decisions when writing your next product description, blog post, or landing page.