I ordered from Steam and downloaded the 10GB they wanted me to get. I then downloaded the update from Steam(which took a while) and launched the client.
Now I have the launcher 'patching'. I don't know whether it's downloading a metric ton of bits, or just very, very slowly checking file integrity and downloading lots of small patches as well.
I've linked a picture, just in case that helps. It's taken 2 hours or so(from Steam finishing everything it had to offer and launching the client) to reach this point.