Sounds like a bad GPU driver. If your ATI card isn't being used, the i3 integrated graphics + processor can't do much more than 20fps on low settings. Make sure to upgrade your ati drivers and everything should work amazingly. You can google how to, you should easily find it!
Also, having 12gb of ram, you sure could launch the game with more ram than by default. You can now change it directly in the game launcher in the profile editor using the "JVM Arguments". (Eg. "-Xmx2048m -Xms2048m" would make the game run with 2gb of ram)
Have fun, Minecraft works like a charm on Linux. I get about 200 more frames per second than I get on Windows.
EDIT (Easier to read than in the comments):
Make sure to delete any drivers first:
sudo sh /usr/share/ati/fglrx-uninstall.sh
sudo apt-get remove --purge fglrx fglrx_* fglrx-amdcccle* fglrx-dev* xorg-driver-fglrx
Then install Catalyst 13.1 running these commands:
sudo add-apt-repository ppa:xorg-edgers/ppa
sudo apt-get update
sudo apt-get install fglrx
That should work, good luck!
file /etc/alternatives/java /etc/alternatives/javac
to your question?