GUITAR -
Okay, so you need a guitar. I would recommend that you don't need to spend a lot of money right now and this guitar from Thomann is perfectly suitable to get your child started. It also comes with a bag, a tuner, and some plectrums - BUY now from this link. Choose based on your child's age.

7-11 years old:

11+ years:

GUITAR STAND -
It's best to keep your guitar on a stand near your favorite chair in the house so you pick it up more often. Otherwise, it might stay in its bag between lessons. BUY now from this link

A CAPO -
"What's a capo?" you ask... it will become clear as you progress through this course. It's a very useful tool to help make certain songs easier to play. BUY now from this link

PLECTRUMS/PICS -
Used to pick the strings of the guitar. They feel strange at first but you will need a whole bag of them since they are easy to lose. You will have some already if you buy the guitar set above but these are the specific plectrums I regularly use myself. BUY now from this link