It doesn't hurt to start them young.

A good starter camera is the Canon A410 (3 meg, 3X zoom). This camera can be found for $130.

Kodak has the C300 which sells for under $100.
It has no optical zoom.

Stay away from low priced no-name cameras.
These are often found on ebay.
They are junk and/or toy cameras.

Many people have had good luck with refurbished cameras. Make sure it comes with a 90 day warranty (or better).

I don't keep up with the used camera market, so I don't know what is available there.