A domain name is separate from the website, which is separate from the hosting.
Think of a website like a house:
- Domain name, i.e. permies.com is the address
- Website is the house
- Hosting is the land the house sits on
You can buy all three separate or bundled together.
Buy a Domain name here: https://www.godaddy.com/domains/cheap-domain-names
Just start typing ideas until you find one that is available. One that ends in .com is the most desirable. Ideally you want something reasonably short and easy to tell someone. Most good domain names are taken, so you will likely spend some time finding one you like. In today's age, you want the domain name and business/organization name to match if at all possible.
Just like a house, you can build your own website, but your results may vary the first few times. I think there are a few people here floating around who build nice websites for fair prices.
Something reasonably easy to DIY you own site would be something like: https://www.squarespace.com/