He or She? His or Her?

Which is correct? Or are both correct? I am writing an article in which I reference the reader's child. I am finding myself writing "his or her" and "he or she", etc. It used to be the practice to write the masculine form to include both male and female. Somewhere around the 70's or 80's, "he/she" and "him/her" began to crop-up amongst the "he"s and "him"s. Then, in the 1990's, writers began using the feminine to refer to both. Is there an accepted form for modern writing? What does the reader prefer, generally? If I settle on a particular set, am I making a statement (if inadvertently)?