Buy the domain itself wherever you want. I like cloudflare, and a lot of people also suggest porkbun.com. You then point the nameservers for your domain to whatever DNS service you want. If you stick to cloudflare then it’s already done for you.

For dynamic DNS I use cloudflare’s one using my router to keep it updated. It’s easy to set up. Depending on your router you may need to run a service on a machine to do this instead. things like pfsense/opnsense should have it built-in.

I prefer porkbun for my domain provider. They’re kind of the darling of the self-hosting community, it seems. But I picked them because they were pretty inexpensive.

I was with Google Domains but switched to Namecheap. They are easy enough to work with and not the most expensive.

Cloudflare for both honestly.

I just set up a wildcard subdomain record and with a few lines in docker-compose Traefik sets up a new subdomain in seconds, certs and all.

They charge the minimum renew amount for domains, plus you can use several different tools like cf-ddns, cfddns, or cloudflare-ddns

Cloudflare if you want one of the handful of TLDs they support, namecheap otherwise. For namecheap I still point the nameservers at Cloudflare so they can manage the site. For DDNS I use DDclient, it works, that’s about all I can or should say about a DDNS client.