AleXx, what you do with the cycled tank is put your filter in a bucket of tank water because you don't want it to dry out, then you would lose your beneficial bacteria. Leave a couple of inches of water in the tank to keep the gravel wet. Put some of your tank water in gallon jugs. When you get moved, just treat it like you are doing a water change. Also, keep any decorations in tank water, too. I hope this helps. This is the advice given to me for a neighbor who moved a 29 gallon tank.
I'm not sure about live plants. And yes, the fish should be put in containers fro transporting.