First off I am all in on Google - whatever you might think of their privacy policies and tracking methods they provide many useful and free services to help companies sell products online.
It's very easy to crack on and hook up Google Tag Manager, Search Console, Analytics and Ads to a website, but at some point you will need to figure out what is important for you to track and customise your setup to make sure you have the data you need.
For example, an e-commerce site is going to have additional and different data points to track compared to a news website. You will need to expose what items are in a basket and their value at checkout at a minimum if you are going to do any meaningful conversion tracking. You could then expand that to include any "add to basket" actions a user has taken, or a users email so you can add them to a negative remarketing list once they have purchased a product.
Most e-commerce platforms will have a place to insert HTML into pages, so you can easily load scripts such as Google Tag Manager, and then load anything else you need in through Tag Manager.
Pretty obvious as it's ubiquitous. My oh my what a lot of data Google collects from us all! Google Analytics is everywhere because it is the best free analytics package.
It also integrates seamlessly with all the other Google webmaster tools below.
I use this chrome extension so I don't track myself in my own analytics if I don't have a static IP to exclude.
Google Search Console
The first thing I would setup is Google's updated Webmaster Tools. It gives you a few basic tools you will need and some tools you definitely need if you care about ranking organically on Google.
It's super easy to connect a site, just enter a TXT record in the DNS of the domain to verify ownership.
Google Tag Manager
GTM was a revelation to me when I first started using it in 2014. With a busy e-commerce site and lots of 3rd party services for reviews, tracking, CRM etc it is much easier to manage through GTM rather than hardcoding into the head or pasting lots of scripts into an admin panel.
Setting up GTM is as simple as creating an account by linking a Google account, creating a container for the website and pasting the code snippet into the appropriate section in the site CMS or directly into the head template.
For this Ghost powered blog I could have pasted it into the Code Injections section of the Ghost admin panel, but I chose to edit the default Casper theme instead. I probably should be creating a child theme here but this is dev.
For a simple site like this GTM is probably overkill (one script loaded through it so far) but for a busy e-commerce site it is very useful when testing new features like site chats or adding remarketing scripts.
There was much more setup involved for a Magento e-commerce site as I had to create a decent data-layer first, so Magento could pass GTM data.
The versioning is very useful and allows to you quickly enable and disable features.
Analyse, predict then test ideas on your website to drive conversion.
Optimize is natively integrated with Google Analytics, so you can quickly understand how your website can be improved.
Google Data Studio
Google Data Studio is a powerful tool to pull together data from different online and on-prem resources and combines them into a dashboard.
You may want to look at a connector to help pull your data sources in such as Supermetrics.
Google Web Dev
A brilliant resource for web devs and webmasters. The measure tool seems faster and more stable than their pagespeed tool (although isn't as in-depth) but gives you a traffic light overview of how Google views your website.
Google uses site speed as an organic ranking signal, and a faster site also results in a higher conversion rate
I use their measure tool daily for a quick check on a web page:
Cloudflare provide protection, caching, DNS and much for for websites. Their free plan has SSL, DNS and use of their CDN.