Google Webmaster Tools(GWT) is a free service that helps you evaluate and maintain your website's performance in search results. It will help you with the Search Engine Ranking Optimization of your website. It offers insights into how it sees your website and helping you uncover issues that need fixing. You will be able to use it for a frequent analysis and for checking the statistics of your website. It gives you precise information how your website is indexed by Google.
You can verify your domain in Google search console which will help in listing your domain in Google SERP. Google provides multiple methods to verify the domain, you can opt the method to verify through Meta tags.