Me personally, as a newb regarding proxy and homelab, I use nginx because it was super easy to set up (proxmox script) there were many tutorials available and it just works great. I had to debug some things and this also worked great, so just a perfect package.

Both Tailscale and Wireguard are valid options but both must be enabled first. If you use a DNS solution to only provide access to HA it always works, no actions needed. I personally use DNS (ipv6.com via DynDNS from my Fritzbox Router) and a locally hosted Nginx to provide access to HA and it works perfectly. If I need access to something else I can still enable Wireguard for full access.