Please see Hardware for options especially you may want to look at the StarLite option
Extending the suggestion by @soundofthunder by setting up your home system to use VNC over SSH - this gives you full access to your LAN having increased security using SSH.
Please note that some ISP doesn’t allow services on privileged ports (port numbers < 1000) so you should run your service at e.g. 33022
You can use the following topic as a reference for setting up secure SSH using public keypair.
And this as a reference to setup your system to serve your desktop over VNC
You can use the following as reference for setting up DNS and router to serve your SSH service to the outside world.