To connect your domain to your IP use godaddy website, it should have a section where you can configure a dns entry, you can specify an IP address (your public IP) and, after a while, every device on the internet connecting to YOURDOMAIN.COM will be send to your home. If godaddy doesn’t offer a dns service you have to buy it somewhere else like on cloudflare, here I think you will need to prove that you own YOURDOMAIN.COM and then setup your IP in the dns. If you don’t have a static IP you need a DDNS (Dynamic DNS). After that you open the port number 443 on your home router so that https requests will be send to a device of your choice, this device will host your reverse proxy, the reverse proxy binds a domain name (the one you brought) or a sub domain to a service of you choice on your local network, doing this you don’t expose the local server directly and you need to open a single port only.

I bought a domain on namecheap.com and it has a configurable dns built in so I hope that godaddy has one too. I use Caddy as a reverse proxy for my jellyfin instance instead of Nginex, I think that they are both valid, another thing other people said in the comment is to access jellyfin via wireguard tunnel and I confirm that is the best choice if you don’t have specific needs, let me explain. The reverse proxy automatically generates ssl certificates using let’s encrypt allowing you to cast from an android phone to a Google chromecast (this seems to be the only way to do it and works very well for me). I also configured other services on caddy, in my setup I block every request to the reverse proxy that doesn’t arrive from inside my local network (except jellyfin so I can use it remotely), I know that it’s not the intended use of a reverse proxy but it makes some things possible that otherwise will need more configuration:

• I have two separate networks in my home, my reverse proxy has a double interface so I can easily access all services from devices on the main network.
• I don’t need to configure local dns rewrites to my services neither I have to add exceptions for dns rebind inside my router, I simply add a new rule to caddy and it just work.
• I have https for every service on my network without annoying messages on the browser.

If you think this lazy use of the reverse proxy could be a problem please tell me your thoughts!

I just recently set up a reverse proxy with Nginx Reverse Proxy, and Cloudflare. I pointed my domain to my home address with Cloudflare (they have dynamic DNS capability), then set up NRP, to forward traffic by subdomain. The nice thing about the reverse proxy it is I can bind a subdomain to an ip:port on my local network. Like “music.!MYIP!.com” goes to my Navidrome instance “LOCALIP:4553”. This allows me to close unnecessary outbound ports.

is the free vpn service the wireguard one? if yes and it is slow, than it won’t be any faster when using your own domain and exposing the server directly to the internet, because wireguard should be as fast as any direct connection. if it is not the wireguard vpn from the fritz box i’d recommend switching to it. this can be done by tge server jellyfin is running on if your box does not support wireguard.

There’s a nice explanation of how caddy reverse proxies work here. https://caddy.community/t/using-caddy-as-a-reverse-proxy-in-a-home-network/9427

Essentially you setup your router to port forward any new incoming connections to Caddy, which then decides what to do with them according to the configuration (Caddyfile).

Even simpler: Your local network is like a castle, inside is a safe and secure place where your devices communicate freely. Your router is a firewall around the castle, by default it blocks incoming connections. This is good because the internet is scary. By port forwarding you allow a door in the firewall which leads to Caddy, which is like a guard. Caddy asks them what they want, and if they say e.g. jellyfin.example.com, then it sets up an encrypted connection with https to your local jellyfin server. If they want anything else they aren’t allowed in.

There’s plenty of reasons why you would not want to have a Jellyfin server be publicly available (even behind authentication). It’s simply not a well-secured system at this point (and may not get there for a long time, because it’s not a focus).

I strongly suggest keeping it accessed via VPN.

But note that VPN access is not necessarily any slower than “publicly” serving the HTTPs directly, at least not by much.

If you don’t already use Wireguard as the protocol, then maybe consider running a wireguard VPN instead, that tends to be quicker than classic OpenVPN.

And last but not least: a major restricting factor in performance of media servers from afar is the upload speed of your ISP connection, which is very often much lower than your download (100Mbit/10Mbit are common here, for example, so only 10% of the speed up than down).