TLDR - download/update to the most recent version of Java.
After much gnashing of teeth today trying to download the game after installing the launcher, I tried all solutions available to no avail. This included port forwarding/triggering, changing my DNS server, rebooting my router/PC, etc.
Still I was only able to download at 20-40 KB/s, which is insane when I have a 50Mb/s connection.
After trying all of these things, I remembered that when I initially installed the launcher, I saw some message about Java, which I quickly dismissed.
I figured, hey, why not download the latest Java version (unfortunately,) so I did. After doing so? 7 MB/s consistent download - 60 Mb/s per the Task Manager, 10 above my "paid for speed."
Not sure why this worked, but I followed the same procedure on my Surface Pro 3 (we'll see how it runs on there) and had the exact same scenario. So it is worth a try!