I think (and this is just a guess), you'll be downloading an extra couple of Gigabytes, I'd say around 5-7GB. From what I've read, after installation it still needs to patch everything since launch. Which is quite a lot, there've been many patches since it's release.
As for auto-download, the way it works after installation is when you open the launcher and log in to your account, the thing automatically starts downloading whatever it needs to get to the current version. It might do that in stages, where it'll download certain files, then install it and then start downloading again. I've read that you can quit the launcher and it'll continue downloading from where you stopped the next time you open the launcher, but I can't confirm that.