First of all you should assess your child interest and need. For example, your child might not use the desk for only reading purpose. She/he might also use it for painting or for any other similar purpose. Once you are sure about age and need of your child, you can help yourself in selecting a right desk for your child. Instead just picking up a desk from the market. Your child might like it at all and is put off in the study.
You should also consider room available in your house, or where you want to place the desk. It can a corner of your child's room, where she/he can study and work comfortably. Generally, children desk are not much bigger in sizes and need little space. It is not guaranteed though, whether your child likes to sit in a corner of the house.
Also think of the material you want the desk be made of. It can depend on the child's age as well. For a child of about 5 or 6 years old, a desk made of hard plastic should do, or else you can buy one made of wood. The wood desks are generally heavier than plastic ones and your child might get hurt while attempting to adjustment its placement. You can also order a carpenter to make a nice desk for your child.
Even before buying a desk for your child, think of safety aspects. For example, in case you buy a desk made of hard plastic, make sure the plastic is not degradable, that once desk exposed to light, its material vibrates into the air. This is unhealthy for your child. Also, make sure that corner of desk are not raised sharply, you can child can get hurt, especially if fallen on the edges of the desk. Properly done corners are safer than raised corners.
It might also help you to accompany your child with you to the shop. She/he might be able to make a right choice for them, and you might need all the hectic efforts, after all. Sometimes, children are clever in making their own choices, and it also helps them in immersing into the environment.