This combination of the above answers solved the problem for me:
performed the Java update:
sudo apt-get install default-jdk
then killed the Arduino IDE and restarted it
my correct board now showed up (Arduino Mega 2560, where before Mega 1280 was only option)
for the drivers, I did this:
sudo chmod a+rw /dev/serial/by-id/usb-Arduino__www.arduino.cc__(a bunch of numbers)
After that, my Arduino IDE shows /dev/ttyACM0
in the tools/serial port menu.
Now, everything works great!