Google now sells domains, as well as email through GSuite.
I use them a lot on new projects, because I find them so insanely convenient, but I can't help shake the feeling that now I'm both the product and a paying customer.
So I'd probably nuance your words with: "select a provider whose livelihood depends on your custom".
And do NOT register it through a provider whose only support is Machine Learning!(tm).
You can the use whatever service you want. G Suite, Exchange Online, roll your own, …
I've used both over the years, though the EasyDNS UI is a bit harder to work with. They seem more technically competent than Hover though, who are decent but not fantastic. ;)
If you buy a domain through Google, you should still be able to transfer it to another registrar.