An at-home pottery kit is built around one of two premises: air-dry clay, which needs nothing else, or fireable clay, which needs a kiln you do not have. Which of the two you are buying is the most important thing on the box and is often the least prominent.
What works at home with no equipment
Air-dry clay, hand building, painting and sealing. That produces decorative objects, models and gifts and requires nothing but a table. It is a complete activity rather than a compromised version of pottery, and most home kits are built around it for exactly that reason.
What needs a kiln
Anything that will hold water, be washed or be used with food. Firing turns clay into ceramic and melts glaze into glass, and nothing at room temperature substitutes for it. A home kit containing fireable clay is really a making kit, and the firing has to be arranged separately at a studio.
Adding a wheel
A tabletop wheel makes throwing possible at home for small work, and it does not change the firing question at all. People often buy a wheel first and discover the kiln question afterwards, which is why the sensible order is to establish where work will be fired before deciding how it will be formed.
Building up from a kit
The natural progression is kit, then a bag of clay and better tools from a supplier, then a firing arrangement with a local studio, and only then a kiln. Each step costs less than the next and the third is where the work changes from decorative to functional, which is the step most people find they actually wanted.
Questions people ask about home pottery kit
Can I do real pottery at home without a kiln?
You can make and finish work in air-dry clay. Functional ware that holds water needs firing, and nothing at room temperature substitutes.
Should I buy a wheel or arrange firing first?
Firing. A wheel changes how work is formed and not whether it can be finished.
What is in a pottery starter kit?
Clay, tools, sometimes glaze or paint and a turntable. Check whether the clay is air-dry or fireable before buying.