1. Sets from toy stores are usually smaller in size. Some pieces are difficult to distinguish, for example Bishop and pawn, King and Queen and etc. Because they are small, it's very easy to lose a piece.
2. Sets from toy stores are often colorful, which is not good for eyes, if your child plays for long hours.
3. When your child goes to a class or goes to a tournament, the sets will be bigger. It's much better to let him/her practice with normal size set at home. Being familiar with the sets is a very small advantage. That's why USCF rule lets black side have the right to choose equipment.
For normal size sets, the board is 20" x 20", with King at least 3.75" tall.
Usually I suggest green board, no colorful piece, black/white or black/yellow. A set at wholesalechess is quite cheap, a little above $10. If you want to support my blog, you could order through the wholesalechess picture on the right side, or click the picture below.