the private IP (which has to take the form of 10.0.1.xxx) to 10.0.1.253

^^^^^^ This is incorrect. the Private IP you are supplying is that of the AirPort, which is NOT the device you want to log into. You need to find the IP address that the AirPort has assigned to your computer. It will be something like 10.0.1.12 or something. You can find it by typing "ifconfig" on your computer.

Basically when you are setting up the AirPort you are configuring it such that:
When a request comes IN on the external address (i.e. 67.177.198.XXX) for port number 22, forward it to the internal Linux Box (i.e. 10.0.1.XXX) which is waiting on port 22.

So: you send a request to 67.177.198.XXX:22 and the AirPort receives the request, and forwards it to your computer on the IP and PORT you specified.

Thank you Avatar and Gilhead. You guys were right, the 67.xxx.xxx.xxx was not my real IP. I finally got my real IP from the "ifconfig" command and put that as the private IP in the port forwarding section. I got stuck because I had to configure it in Windows and it assigned a different IP when I booted up Windows as opposed to Linux, so I had it forward the request to the Windows IP, instead of the Linux box. Once I found the Linux IP, I forwarded it to that address, and everything worked like a charm. Thank you soo soo much. I would have been lost without you guys

Glad to help