As a former optician (the person that would be teaching your kid how to put them in, take them out, general care) I want to let you know that it greatly depends on the maturity of your child. There were 12 year olds I had to teach that were totally ready for it, and there were 18 year old kids that I had to say - yeah, you're totally not ready for this. maybe try back in a year or two. (couldn't wash hands properly - how hard is it to rinse the soap off of the fingers you're about to stick IN YOUR EYE?!?!)
Anyhoo - if they Dr deems your child mature enough, they will be fitted for contact lenses. Like shoes, some may work better or feel more comfortable than others. The fit is dependent on the curvature of the cornea (the clear part of the front of the eye) - this is called base curve, the moisture level/dryness of your kids eye, and the type of prescription your kid has. if they have astigmatism, they may need a Toric lens, which is slightly weighted at one end to give the vision correction at the correct spot in their visual field.
Also be aware that the first time your kid is fitted for contacts by a Dr, they will normally be charged a fitting fee. This is aside from the normal eye exam. It will probably also include a follow up appt, so that the Dr can check the health of the eye after wearing a contact lens all day for a couple of days. Contacts do effect the eye, decreasing the oxygen levels of the cornea, and exposing the eye to more/different bacteria. Contacts also make your kid more subject to infections (touching the eye a lot, introducing bacteria in the eye, etc) and can lead to serious problems if not properly taken care of.
Do NOT take this decision lightly. Discuss it with your eye care professional and see what they think. The industry "standard" age is 12, but there are Drs out there that will do it at younger ages if they feel the kid is up to it.
So, in short, although you priced $60, that may be cheaper or more expensive than what your kid is prescribed. Only your Dr can tell you what may work best. After you have a prescription, you may be able to shop that brand/Rx around.