"Encrypt the IP" is technically nonsense. An SSL-encrypted https TCP stream is still a TCP stream, and the connection cannot be made without IP addresses. Everyone in the position to observe the traffic can easily log the source IP, source port, destination IP, destination port, and bytes sent in each direction. What gets logged and for how long depends on who's watching, and whether they are compromised or acting under a subpeona.
Assuming you are connecting to a WiFi access point which in turn is connected to an ISP which is routing your traffic across the backbone to your hosting ISP which is providing a virtual or co-located host, this boils down to:
- Your WiFi router (and everyone also attached to it) can see:
- Your MAC address, which identifies your physical hardware uniquely.
- Your server's IP, port, and how much traffic you exchanged with it.
- Your router's ISP (and the network backbone) can see:
- Your router's public IP. If this is a US residential connection, they likely log the public IP and the account holder and maintain those records for 6 months.
- Your server's IP, port, and how much traffic you exchanged with it.
- Your hosting company (who likely knows who you are) can see:
- Your router's public IP, port, and how much traffic you exchanged with your server.
If you want to hide your connection to it, use Tor, as mentioned by MadHatter. Everyone up to (and including) the Tor entry node can know you're using Tor, but not what you are connecting to. Everyone after (and including) the Tor exit node will know that a Tor user connected to your server, but not who.
Under normal circumstances, there is some danger in a compromised exit node logging or modifying the contents of your session, but that is mostly mitigated using SSL.
If you want to further hide your server, set it up as a Tor hidden service. In this case there is no Tor exit node, and it may require shell access to your server to even identify that it is running a web service, particularly if you also configure it as a Tor relay to mask the traffic. You will then need to access it as https://blahblah.onion, so your PC wouldn't even know the IP from your web access.