Excuse me, what is suitable for a small studio to buy a medium telephoto? kids photography

50 mm lens, back to the end, can't you shoot the whole background? I don't think so. Your background should be on the wall of 4 meters, and the child is about 1 meter away from the background. You still have about 5 meters. 50 mm head should be enough.

Do you still want a medium telephoto lens? If you can't play with 50 mm, isn't it more difficult to play with a 70 mm head?

Your lamp is a little short. You need at least one background. For balance, you need two. People have four main lights and auxiliary lights.

However, your studio is so small that it is really not fun. Just go to the smallpox track, save a lamp holder, and then fall on the children, and the business will be ruined.