The best pottery kit will depend on your ability level and budget for purchasing the equipment. A beginner potter may want to start with a less expensive kit that includes only the bare minimum of equipment necessary to get started with the hobby, while an intermediate or advanced potter will want higher-quality equipment. It is a wise decision to start with a less expensive, basic pottery kit if you are a beginner, since you do not yet know if this is a hobby you will want to stick with. If you are sure of your interest in pottery, consider a higher quality kit.
Consider, too, the age of the person who will be using the pottery kit. Special kits are designed specifically for children, and the pottery wheel is likely to be small, lightweight, and designed with safety in mind. Small children can play with the clay and begin to develop an affinity for the craft, and parents won't have to pay a significant amount of money for the equipment. Such a pottery kit can be made from lightweight plastic, in which case it is likely to be considered a toy; older children with more dexterity and patience may benefit from a heavier-duty kit that is not considered a toy but is not necessarily considered a professional kit either.
It is a good idea to research the different types of equipment used in the pottery making process. A pottery wheel is the key component of any pottery kit, and many types exist. Perhaps the most commonly used wheel is the electric wheel, which can be plugged into an electrical outlet. The speed of the wheel can be varied using the accompanying controls. Vintage wheels may be powered by a foot pedal; this will require more coordination and effort to use, but can also be quite fun.
Most kits will not include a kiln, or oven, for firing the clay once it is fashioned on the pottery wheel. This means you will need to find a way to harden the clay another way. You can invest in a pottery kiln, but this can be quite expensive. Some clay can be fired in a conventional home oven, but this is not always the safest or most effective method. An alternative to either option is to use a kiln owned by a local potter, or if possible, at a local community college.