There are two things that I recommend when you are doing domain settings with Squarespace.
The first is to change your built in domain and the second is to connect a third party domain.
Change your built in domain
Changing your built in domain makes your squarespace url way easier to remember and fits in with your brand. Usually the Squarespace built in domain will be a bit random so its nice to be able to customise this when your building your site.
Settings>domains>built in domain>change the domain>confirm and the page will refresh.
You should be able to see in your website url bar that it is now customised.
Connect a third party domain
Its a good idea to use a third party domain provider for a few reasons.
You can pick anyone you like and they usually have other services attached
More options to choose from
Prices will vary slightly
But how do you know which domain provider to pick?
What you need to look for when picking a domain name provider are a few things
The support - do they have online chat? or Can you call
The interface - is it easy to use
Does Squarespace have instructions for it
What will the installation be like?
If your totally new to setting up domains go with Godaddy as you basically have a one click install and its very simple.
If your a bit more confident with domains and can follow Squarespaces instructions go with Only Domains or one of their listed domains that has instruction. The process is a little more manual abut again you have more choice.
There are quite a few different instructions on setting up your domain with Squarespace depending on what provider you chose. I recommend checking out their detailed documentation for each one.