Once the game is installed form original disk and then the remainder from Steam do I need to continue to have the disk in the pc to run the ga,e or can I run the game without using the disk ever again?

On the PC you do not need the disk at all. You do not even need the disk to install the game since Steam will download and install the game.

If you choose the disk you get the first 5GB+ installation files much quicker, but the remaining 18GB from steam (over the net)

If you run the game first time with an internet connection and you choose offline mode, you don't even need to be online anymore. !!!

And yes, after the installation procedure (if you choose to install the first part from the disk or not) - you don't need the disk anymore, the game will run from this point on from the Hard disk. Just keep your disk safe...