I have Bettas, and have moved them several times. Here's what I do:
I haven't tried transporting many plants, but the few that I've had, I just put in a plastic bag of tank water, then stored it in the cooler with the fish. If you have a lot of plants, perhaps put them into their own cooler?
- Each fish goes in its own plastic cup. (Bettas need to be kept separated.)
- Put the cups into a cooler. Use newspaper or plastic bags to fill in any spaces. This will keep the cups from sliding around.
- Put the cooler on the floor of the back seat. Being on a flat surface lessens the chance of spillage. Being within the car itself minimizes temperature fluctuations, since I can alter the heat/AC depending on the outdoor temperature.
- Put a half-filled water bottle into the cup holder next to you. This will allow you to see what's happening with the water in their cups. (Also, it's good to drink when you get thirsty!)
I haven't tried transporting many plants, but the few that I've had, I just put in a plastic bag of tank water, then stored it in the cooler with the fish. If you have a lot of plants, perhaps put them into their own cooler?