MacOS – Connection very slow on Mavericks

I have a Macbook Pro middle 2010. I had Mountain Lion till yesterday when I decided that today I would have "upgraded" to Mavericks.

With Mountain Lion everything worked fine until 5am tonight when I last used the wifi on that operating system.

So I backed up few files that I really needed and made a clean installation of the operating system. Everything went exceptionally fine and In a matter of an hour I found myself logging in into Mavericks.

Everything else works fine (as far as I can tell) but downloads and everything that it has to do with the internet connection is very very slow. The symptoms are:

• Downloads started from browser often don't start on a lot of websites (Minecraft.com, Utorrent.com, etc). They are shown as they going with 0Kb/s for an hour or so). This happens with both wifi and ethernet connection.
• YouTube videos refuse to load (the page loads, but the video stream is stopped at the beginning and doesn't go any further, ever) with wifi and loads very slowly with the ethernet connection.
• Minecraft updates or dropbox synchronization are very very slow (takes hours to update few files or download the recent snapshot) even with a 7MB/s connection.
• Speedtest.net says I have a download speed of 5Mbps and a ping of 72ms.
• The Stack Overflow chat works very badly. Messages are synchronized slowly within long periods of time and messages sent by me are shown 2 times or shown in green (which means they were not really sent).
• The Wi-Fi connection doesn't give me any error messages, and generally no particular messages are shown at all.

• In Safari downloads start but they don't go faster than 2Kb/s.

  

In the meantime here's the status of uTorrent:

And here's the status detected by Speedtest.com:

I've never had any of such problem earlier. I can recognize that there's a 5% chance that these problems are something else related, but to be realistic, I'm pretty sure that it is Mavericks or something linked to it.

How do I fix these problems?