Hi shox,
This is probably a bad idea. There are, relatively constantly, automated scans looking for "open" ports (for example:
https://www.shodan.io). If you enabled full access to your home computer to the Internet - expect that your computer would be taken over in short order. While there are many layers of security you could potentially add, one that is lightweight that may help here is to port forward to an ssh server (port of your choosing...that also works).
So the network diagram may look like this:
+----------+ +--------------+ +-------------+
| Home | ----> | modem/router | ----> (Internet) <---- | Your remote |
| Computer | +--------------+ | system |
+----------+ +-------------+
You need to choose an appropriate authentication mechanism on your home computer (username and password alone are probably not sufficient...ssh keys are one relatively easy way to go, depending upon how you plan to use this). Additionally, your ssh server is configured to
AllowTcpForwarding yes.
When you are remote, you connect to your host name on the port of your choosing by using an ssh client (openssh, putty, others...). You will need to configure it to open a "tunnel". Here is an example configuration summary from putty on Windows:
Connection -> SSH -> Tunnels:
Local ports accept connections from other hosts (unchecked)
Remote ports do the same (SSH-2 only) (unchecked)
Source port: 127.0.0.1:5900
Destination: 127.0.0.1:5900
Local (checked)
Auto (checked)
(Don't forget to "Save" in Putty, or you will need to reconfigure the putty client from scratch.)
But...there are 1000 ways of answering this. The above is relatively easy to obtain software for across Operating Systems, should work with your current setup, and doesn't take long to configure.