All of my baskets are currently made using commercial reed and cane and commercial dyes and are thus considered contemporary baskets. So these tips pertain to that style of weaving. I've tried to keep the weave as traditional as possible, since I'm Cherokee, that's important. As with all artistic endeavors, you'll find that the basketweaver will have their own style in weaving the basket, so there are many ways to begin but a Cherokee Basket will always look basically the same.
The cane is the same that is used for chair caning. Although you can use the natural cane, which has the outer hard skin still on, I have found that using the Hamburg cane gives you a much tighter and even looking basket. Hamburg cane is that cane which has been bleached and stripped of this outer hard skin or shell. This type of cane is used in making the contemporary Cherokee Double Woven Baskets. Although you can use flat reed or oval reed to make these and in some cases, this might be the preferred material of choice for a beginner. It is however, the cane that look closest to the River Cane used by SE Cherokee in Ancient times.
Reed is used in making the Oklahoma Double Wall baskets. Reed comes in a variety of sizes, but the size to start with is the #2 round reed. The smaller size of round reed will break very easily even when wet, so not real good to learn on. Cherokees began making this type of basket in OK, after the Trail of Tears.