When parking do you put the emergency brake first before you shift it in park?

Fantastic question!!. Yes you do. The reason is that 'Park' puts a mechanical lock on the gearbox, a bit like puttig a stick through the spokes of a wheel. Putting the whole weight of the car on the park dog can make it wear excessively resulting in the gearshift jamming, especially when parking on hills. A lot of people never set the emergency brake and, without exercise, the linkage seizes up. Then what braking have you got in an emergency? Zip