At what age is it appropriate for children to begin reading the Bible on their own?
I would begin training a child in the Scripture while they are yet in the womb - even before (Jer. 1:5; Luke 1:41; cf. Gen. 18:10-15). Mother and father alike should read to them and even later when they are in their crib.
As they grow, I would continue to teach them the Scripture in family Bible studies (Deut. 6:4-9; Eph. 6:4), church (Heb. 10:25), etc. While continuing family devotions and church, depending upon the child's development, at approximately age five or six they should be able to read the Bible on their own. I observe this principle in 2 Timothy 3:15 which says, "... how from childhood you have been acquainted with the sacred writings, which are able to make you wise for salvation through faith in Christ Jesus." I would add to this the family's memorizing of the Westminster Shorter Catechism together (see link below).
A good children's Bible is the Child's Story Bible by Catherine F. Vos. When they are mature enough, I would encourage them to read the NKJV or ESV.
Dr. Joseph R. Nally, Jr., D.D., M.Div. is the Theological Editor at Third Millennium Ministries (Thirdmill).