You need to make sure you get a unique public IP from your home ISP. Some utilize a so called CGNAT which allows them to share one IP with multiple customers, but this makes self-hosting from home much more difficult. Less bad is a so called dynamic IP, which is unique but can change randomly. For that you need some system to automatically update your DNS records when a IP change is detected.

And yes, the domain registrar and dns server operator has an webinterface to associated your public IP with the domain name. The better and larger ones also provide an API to automate it should your public IP change.

There are many things you can do to improve security, but mostly you should run a firewall to not expose any internal services to the public internet.