I tend to favour using .ca domain names. They generally have better availability and it supports local registrars.
How to Point a Domain to Your Home Server
None of the links on this page are endorsements. These are services I personally use and that have worked for me.
Find a reputable registrar and secure the domain name.
My favorite registrar these days is Baremetal.com a registrar I started using because they offer cheap .ca domains. I keep using them because they’re simple, never try to up-sell me on other services I don’t need, send me reminders with enough notice that I’ve never lost a domain to renewal timing, and give me the opportunity to add a bit in for charity every time I buy new or renew.
Find a reputable DNS service and register your new domain.
I’ve been using Zoneedit.com for a couple years. When I signed up they offer a single domain DNS service for free, which is enough to get things set up and make sure they work for you. I manage 6 domains through them now, and their credit system allows me to pre-purchase a year’s worth of banked credits at a discount and they are all applied to the account as needed. They also offer some basic configuration tools that let me add a handful of email alias/redirects, which means I can have simple info@-type addresses that point to my main gmail account.
Under construction, still writing.
Update your registrar domains settings to point to the new DNS service.
Update the DNS service to point to your home server IP.
Use port forwarding on you router to point incoming requests to your server.
Configure your server to point incoming domain requests to the directory where you keep your files.
Use a DNS updating tool to regularly and automatically update the DNS service.