How many gigabites is Team Fortress 2 On the computer?

It really matters on the updates, maps, mods etc you have.

and if you are including the memory taken by Steam (which isn't very much)

Everyone has to download pretty much the same amount. The earlier you download it, the more updates you go through. The later you download it, the more you have to download due to updates. Currently, 18/03/2012, there is approximately 11-12GB amount of downloading required to download the game entirely from the beginning.