Hi, Jenny and welcome to the forum :) It is fun growing fig trees with kids and then try the fruits together :)  My youngest one usually tries to beat me to the ripe ones :) Two of my daughters love sweet yellow honey figs with tender skin. I would highly recomend Conadria and Italian Honey .

Gene, I am curious too where in Middle Asia you are from and what is the closest fig variety in USA that resembles Sari Zybek ?  I grew up in Middle Asia , Kyrgistan, among beautiful fruit orchards, green forests, mountains and  gorgeous Issik-Kul lake :)  So many wonderful memories from childhood are connected with gardens and nature and eating fresh fruits right off the trees. All my married life now here in USA I am trying to create the same thing I had, or at least a little portion of it, for my own kids so that they can have those wonderful memories and can experience what it means to climb a tree and enjoy fresh fruits :) We grow so many different edilbles in our garden here in hot AZ desert... it is so much different from Middle Asia :) 
Two of my daughters love sweet yellow honey figs with tender skin. I see Sari Zybek fig trees on sale sometimes on Ebay, but since I have not heard much about it, I never got brave enough to try growing it here. Would be great to know what  fig it resembles and if it likes hot dry climate like ours :)

My kids were eating figs and all sorts of fresh fruit when they were less than a year old. They prefer fruit over any candy or chocolate. As far as what varieties, it really doesn't matter much, but they're now 6 years old, and they know  exactly which one have the best flavor. They wait to let it fully ripen and they pick them off. 
As far as what varieties, they love Celeste, Hardy chicago, Dark portuguese, Brooklyn white.