where can I get a low cost pottery wheel for a beginner

If ur 12 year old has never done pottery the most low-cost way is find a class for him/her. If they turn out not to get enthusiastic about wheel throwing u do not have a wheel nobody is using around. Also u do not just need a wheel, u need to deal with the clay, glazes & kiln for firing as well. Also, unless u personally have experience, the child will have much more fun with a teacher. Teaching yourself to throw pots can be a rather frustrating experience.

If u r teaching yourself I would check classified ads, craigs list & ads in pottery store for a second hand wheel. But even if u can teach yourself, u still will have to deal with firing, so I still think a classes is the way to go.