You will see a demo store > Go to admin > create account
Set Account name & property name, feel free to use the name most relevant to your website,
Set the time zone & currency
Add your website details
Add the Urchin tag using Google tag manager, if you are using a site builder like wix use a global tag manager
Google Tag Manager
Type account name, select country, website address and target platform
Google will give you a tag like this to install, you can forward that to your website developer.
Above is the basic setup for installing Google Analytics.
3rd party tools for analytics
If you are looking for more intuitive options, you will find companies like SEM Rush, AHREFS, MOZ, however they are paid. Although provides an easy interface with a plethora of options in the form of metrics.
What you should ask from your Web design company?
Providing analytics to the customer is by default and is a must for search engine optimisation & marketing both.
However, consultancy on analytics depends on the digital marketing package.
If you are signing up for digital marketing services with exhaustive reporting or DIY reporting via Google or consultancy on reporting too.