Disregard the sloppy gameplay in the video, without screencasting, everything will run smooth.
You need to install Sun Java 6
sudo apt-get install sun-java6-jdkThe most important command i used is
sudo update-java-alternatives -s java-6-sun because even if the the sun-java6-jdk/jre is installed correctly, another jre/jdk like openjdk may be the preferred version of java, preventing Minecraft from starting.
The command will set SUNs JRE as the default one and evade problems.