I will be moving a computer soon and I have everything ready to go aside from packaging. Cpu heatsink, and graphics cards are removed to prevent strain damage, and everything else is secure (I will be transporting myself). Typically I leave the mobo, cpu, drives, RAM, and PSU in the case, then repack everything into the original packaging the case was shipped in. In this case (corsair 600t) it's a fabric type slip bag and two styrofoam blocks to secure it in its cardboard box.
I never thought about this before, but can carting around the PC between the styrofoam cause ESD damage? Or will the case protect it? No circuits are exposed, and everything is in the case where it should be.