Good review on the basic 9 Essentials. I always carry the 10 Essentials Plus. Boots are the foundation of Mountaineering, and that was first very carefully selected item I purchased from a knowledgeable sales person who actually went to a school and learned how to fit boots to the person. The boots never let me down.
Helmets are recommended for the hardest 10-15 or so peaks, but are not really needed for most 14ers. We cover them in the "Additional Useful Gear" video, along with ice axes, traction devices, trekking poles, etc.