If you want to have a website, you need to have a domain name. No doubt about it.
When choosing a domain name, it is best to choose them in this order: .com first, then .net and then .org. If your business is local to your country, then you could also consider country-specific ones as well, such as .ca (Canada), .co.uk (Great Britain), .com.au (Australia) and so on.
There are lots of other Top Level Domains (TLDs) to choose from, but the .com .net and .org (and their country-equivalent versions) are the ones that will get you better rankings in the search engines and are most trusted by internet users.
As with hosting, there is a plethora of domain name providers out there. If you looking for domain name ideas. all of them will have a tool on their website which will allow you to try different combinations until you find one that is appropriate and available.
Yes, that is an affiliate link, and I will get paid a commission. But if you do decide to purchase a domain name through my link, you will also get an hour of my time to help you do whatever you need to do to get the domain active, including hooking it up to a hosting account. Just contact me, and when I verify that you have purchased, I’ll be in touch.
Note that I do not recommend purchasing hosting from the same company which supplies your domain names. That can be fraught with problems in the future. It is best to keep your hosting company and your domain registrar as separate services.
BONUS! If you purchase hosting through my recommended service (another affiliate link), you’ll get another 2 hours of my time to get everything going. That’s a total of 3 hours! See my Hosting page for more details.
Be sure to contact me if you run into any problems with the domain name or hosting purchasing process.
Here’s that link again to purchase hosting: NameCheap