Cane sugar is fine, and honestly most restaurants use plain white table sugar, but there is a richness that unprocessed sugar provides that compliments Chai much better, and demerara or cane sugar are gonna be much friendlier than white sugar. Cardamom may be hard to find in your area, but it's crucial. Usually they will be in a tiny glass jar and very expensive, but if you can find them at an Indian store you can score a half pound for the same price.