We have a few guitars that we often recommend to beginners, and know are good quality, easy to play but excellent value for money. See the list of recommended guitars here.
You are sometimes welcome to borrow a guitar from the tutor for the first lesson or two. However, you wouldn’t be able to have it at home to practice, so wouldn’t get good value from the lessons. Also, we are unlikely to have guitars that are a good size for children to play.