Full sun is general 8 to 10 hours a day. Can it work with less? Yes, but your yield will be reduced.
You could start them in a container for later transplant but make sure the container is as big as you can find. Your kitty litter tubs would be probably work but if you can find bigger it's better. Rhizomes will spend the first few weeks developing roots. Whatever container you use, put lots of drainage holes in it. I use a 1/4 inch drill bit and put holes in the bottom and also around the sides a couple inches from the bottom. This allows for drainage even if you get a spring shower that overwhelms the pot with water.
Good luck on getting your house!