Hi,
You have come to the right place!
I have 11 houseplants in my room at university now, and will be having the same issue when I leave for Summer.
To be honest, they usually travel fairly well if you squeeze them in tightly next to each other in the footwell of a car, so they don't really have enough room to topple over and spill/get damaged.
Alternatively, you could buy a shallow sided crate/box of some kind, then pack them into it and put this in the boot of the car.
These tips only work if you are travelling by car, I have no idea how I'd do it if on a train/bus!
Hope this (kind of) help!
Abbie
University of Southampton, Postgraduate Ambassador