Google Webmaster Tools - This allows you as the owner of your website to see the site the same way the google crawler will see it. To minimize the "crawling budget" that Google needs to analyze your website, the WMT service will help you optimize your website, and provide more detailed insights into search data from your visitors.
Google Analytics - Start with the foundation that many other tools rely on. Even if you can now find alternatives with similar functionality, it's still critical to run GA since it's integrated with so many other tools like your Marketing Automation system. Make sure to do the basics like setting up the right IP Filters and Views, and at least 1 conversion event.
Google Tag Manager - As you implement GA, you might as well implement GTM at the same time. It saves you doing it later and will allow more extensive tracking of visitors as they move through the funnel. GTM also incorporates the GA tracking code that you need to add to your website HTML pages, so you don't need both (and this saves page load time).
Google Optimize - Your first experimentation platform. Free, and a good starting point before you start paying for products like Unbounce or Optimizely.
Google Data Studio provides great dashboards and reports based on the data from the previous tools. Combined with Google Sheets it provides a great toolset to start turning your metrics into scorecards that help manage and optimize your marketing function.
Google Adwords - At some point, you'll consider running ads. Retargeting, display ads or other Google PPC products. It's good practices to implement Adwords right away and make sure the setup is connected to your GA account. Ideally, you align the conversion goals you set up in GA with what a conversion of an Ad in Adwords means.
Where does Google 360 fit in? At $150k/year you will likely not start by implementing the premium version of the Google Analytics suite. At some point though, it could start to make sense. The details and accuracy of information are very high and still much stronger than many other paid alternatives.