It's a pretty large download, to get your local installation updated to the full server version. I'd guess somewhere between 1-2Gb. However, if you get hold of someone with a recent update, they can send their DAT file to you. Depending on how many chapters (or expansions, if you like) they have, it can be up to 5Gb. So it would be worthwhile to plug a HDD in rather.
Note that you can also just install the game and let it run its initial download, which is approx 500Mb. Thereafter it can trickle the rest in the background whilst you're playing. However, on anything less than a 512Kb connection, this can occasionally cause lag whilst you're playing. I recommend installing the game, registering your account and then either running a dedicated update (meaning the 1Gb+ download) overnight, or grabbing a DAT file from a friend.
NOTE: when I first got ADSL and my PC's IP address changed, I had some issues getting the update to work. Hopefully this isn't a problem anymore.