yes that is the right kind of tote, you would need the solid plastic ones so its not see through. and thats a small one, they have bigger ones, you want the ones that are like 2feet by 3feet and like 2 feet tall. so stacked up it would be about 4 feet tall, the lids are un needed. that box could work great too tho. the plants on average when done are at least 2 feet tall up to... well 5,6,7,8... depends, i dont think you will be getting plants larger than 2 feet if you are flowering early.
k man, if you have a closet that right there could just be your container, it would alow more air movement and space. forget the totes, get some heavy duty 3-4 mm thick black sheet plastic, white too. they should be sold seperately at walmart. just layer the white over the black and line that half of the closet with it, secioning it off from the rest and making sure not to leave light leeks or open areas in it. ill post a few pics of my closet setup, i have a space just like the one you are going to use. a few of the pics are sideways just cuz i couldnt get the whole thing.
i use the shelf above it to store my ballast and bulbs along with other supplies i have.if you would want to get into cloning that would be a great place. since you dont have any ballast to worry about, and the shelf would be warm cuz of the lights, so that would help the clones. just make sure that durring the flowering phase that there are no areas light can get into durring its night cycle.
if you still want to use the tote idea that pic you drew up looks great man.