It is real pain taking it around. I have already broke 1 2001FP while traveling.
You simply need to pad it to the extreme.

With the BETA version of Party you no longer need the extra screen.

But to answer the question you asked:
Backpacks are not best. One of the rolling (rectangle shaped) cases works best. With the rectangular case, it is easier to place the monitor flat. With backpacks, I find the necessary support isn't provided.

Also note that when traveling on budget airlines with the 2001FP you will probably be put over the allowed luggage limit. This leads to extra fees.