Handstand-first is the opposite of the order in which they are usually taught in Iyengar practice, FWIW. Headstand and shoulderstand are staples (intensively taught beginning at Level 1, with lots of props, always together) and full arm balance is later. It’s true that the head and neck are important to position right, but (if the 70-yr-olds in my Iyengar classes are any indication) most people’s ability to do that far outstrips their ability to hold up their body weight using arms and trunk.