We recommend Jute.
The most common for many rope tops are jute or hemp (all natural fiber ropes), also popular is silk rope. Jute is a naturally strong and compact rope, but it can sometimes bristle. When it is well conditioned, Jute can feel amazing to be tied up in. Hemp is naturally smoother (and often has a little smell to it), and when it is conditioned well it can feel incredible to be tied up in. Silk is perhaps the most expensive of the choices, but it is smooth and — literally — silky quality make it strikingly beautiful to be tied up in. Finally, some rigging (suspension) uses synthetic ropes that are made to feel like natural rope, including Hempex and POSH.
For very beginners, we recommend jute.
Nylon is OK for the beginner section, where you can learn some very basics, but not suitable for Shibari. We recommend against cotton, for either the basics or the floor work.
If you have any synthetic rope (like nylon) lying around the house, use that for the beginner section before you invest in a set of ropes. When you are ready to invest in ropes, we recommend you purchase four to six 30′ foot (or 9.1 meter) as well as two 15′ lengths of rope to start with Shibari.