Nextcloud is fine without Anubis since everything is behind a login.
Yes, you need a reverse proxy. Also you need a public IP which not all ISPs offer. If you have one, you have to forward port 443 to the reverse proxy in your router config. That means someone who tries to connect to your router on port 443 will be forwarded to the reserve proxy who checks which domain was looked for and forwards to the actual Nextcloud.
You'll need a domain pointing to your public IP. That IP may change, so you need an automation that updates the DNS records (known as dyndns). When you're selecting a registrar, look for one that has dyndns support (you can use different nameservers but that's unnecessary extra steps).
