How are you connecting to the web site now (from outside your LAN)?? If you have a static home IP address (for the internet side) and have a domain name routing to that address, do you have your router/firewall forwarding requests coming in on 80 or 443 to the local IP address of the web server?

Also, what reason are you thinking you'll need to connect to the ESXi host (or vCenter) server?

If you have a router with VPN capabilities, then set that up for access. If not, then if you open up ports, and perform alternative forwarding, you could leave yourself open to attack.

At one point, may years back, I hosted a web site and ftp site in my home lab (could connect from outside my home network). I used the DYNDNS service to forward URL requests to those VMs (they would forward to ports I specified, and then my router would do port forwarding to the correct target). I'm no longer doing that since it's safer, easier, better to use an externally hosted website. Plus, with DropBox, Google Drive and OneDrive, I have plenty of space to put things I MIGHT need to gain access to while not at home.

If you feel you need to connect to the host due to the website server needing reboots often, then you have something very wrong with that VM that should be fixed. In the years I ran a website from home, I very rarely rebooted it (it was running Linux). I had things go offline more often from power outages than needing to reboot the VM.