Just like all natural oils you should also store castor oil in dark and cold place. It don't have to be a refrigerator but if you have extra space inside you can put it there. It is good enough to put in pantry because in there is cold and dark enough. If you would left in some bright space, in time it would start to smell and you would loose some good properties. If you would left it in very high temperature, vitamin E you be destroyed because in high temperatures vitamins do that. What ever you do, don't ever leave castor oil bottle on direct sunlight!
It's best to keep it in glass bottle!
As for bottle, castor oil in pharmacy is sell in small plastic bottles. And that is totally OK! But, nothing can compare to glass! If you can, buy small glass bottle and pour castor oil from plastic bottle into glass bottle! Color of glass is no matter to as. It is also important to keep bottle closed so that air has minimum impact on castor oil!