You can use any version of the original Robotics Instruction Set (RIS) with this brick: 1.0, 1.5, or 2.0. There is also one release of software from LEGO Education that was the last that supported the RCX brick, but I don't know much about that. Any of these will work with the brick you have.
These releases are Windows only, AFAIK. If you don't run Windows, your biggest hurdle will be getting a Windows VM working with the serial or USB IR tower.
It will upload the latest firmware to the brick, so even if your brick says "1.0" on it, it will accept any version of the bundled (or supplied by you) firmware. That is, firmware versions 3.09, 3.28, 3.32 will all work on the original RCX 1.0.
So, my advice is to find a copy of RIS 2.0 for your son. You should be able to find it on eBay or Bricklink.
I see there is another answer that attempts to help you find the RIS 2.0 package.