I had to have an easy one because dang, why not! I seem to see a lot of discussion around domain registration in a few WhatsApp groups I belong to with entrepreneurs. I've formed some strong habits with respect to domain registration over the years but there are some neat things to also consider as you try to nail down registering for a new home for your future work.
Branding and availability
Availability of Facebook, Twitter, Instagram and other Social "handles"
Easiness of spelling and pronunciation (from the guy who chose "Foliofficient" as his last business name)
A note on these considerations is that when I'm doing some searching for my domain I'll usually do some brainstorming with a Dictionary, Urbandictionary, and Synonym/Antonym checkers. I also tend to do a Facebook, Twitter, Instagram check before I buy my domain names to make sure I can snag that vanity URL at the same time.
I'm gonna seem biased, but I migrated away from another service to this service a long time ago. Their web interface has grown quite well over the years and is secure and managed via two-factor Google Auth if you want. This is super useful in the event you want to make sure your domains stay yours.
Most of the .ai, .io, .xyz, .com, etc are all very reasonable here and at many times when compared to other registrars a bit cheaper. I promise that if you are buying a domain name, the actual purchase of it is a commodity and the after-you-buy experience is what matters. They have great tools for managing the domain records through Advanced DNS (free by the way) and if you have to setup Gmail / Google Workspace it's like 2 clicks in their advanced DNS to set up.
I saw this post on Twitter a few days ago and had to mention this because it seems so useful. Steven Tey founded oneword.domains after a bootcamp as a project and generated a reasonable return for a small 1-person business. He now works at Vercel (which I mentioned in an earlier post). I'll definitely be giving this a shot next time I'm going through this exercise, as I want to generate a non-english but easy-to-pronounce and use word for my next attempt at a startup.
Another huge plus for this tool is that you are supporting a founder and he will be having you complete your purchase on Namecheap.com. I'm definitely using this next time in my brainstorming ideation process.
These are the folks I used for like at least 10+ years. They are one of the first places we could register domain names back in the late 90s and have added a lot since then. They tend to be expensive, and once I discovered Namecheap after some failed usage of Godaddy I stopped using them. I can't give you a good reason to choose this, but it's worth looking at your domain name here to see if by chance it's cheaper. They are a fine provider if you can save a few bucks, however, it's super unlikely.
Things to avoid or be aware of
Google's domain registration may seem easy however their DNS / Advanced DNS tools are horrid to use, and if you build out your website with Google Pages you may be stuck with them. There are many deals where you can buy something like Namecheap and get Google Workspace set up through Namecheap. I've done this before, I'd suggest avoiding it, just go buy Google Workspace through Google. It'll be easier to administer and hand off to a DevOps person later.
Squarespace and Wix and generally any hosting provider probably have some shortcut to help you "save time" by supporting the purchase of your domain through their host. This is a short-sighted decision and won't scale once you start using AWS/GCP for other services. Just use a domain registration service that does next to nothing but manage domains.
Beware Elephant Killers
I want to make it abundantly clear that some businesses out there may have Leadership that doesn't align with our values. Albeit I am a capitalist, I believe that hunting elephants and other endangered species have no place and definitely should not be something I send my money to benefit.
I will not link to their website by the CEO of GoDaddy has been known to hunt endangered species and advocate for the proliferation of such practices.
I avoid all GoDaddy services as a matter of principle, and if you so choose to use one you should know that you are supporting this person. Bear in mind Godaddy has sub-brands like Dan.com - you can always leverage their search capabilities, and buy somewhere else.