I thoroughly recommend the D&D Starter Set : https://www.amazon.com/Dungeons-Dra...786965592/ref=cm_cr_arp_d_product_top?ie=UTF8
It's cheap, has the basic rules and has one of the best adventures written for D&D in modern times. My D&D veterans I have played with for the last 20 years loved it, and so did my 10, 8 and 6 year old kids who had never played before.
I agree with this. The starter set and it's adventure are awesome. I was asked to run a game for a friend of mine and his 13 year old daughter, and I used the Starter Set. The experience was inspiring enough that she started her own game with her friends.