It really depends on what car you have. If it already has very good handling and braking then why not do power first? Theres no reason not to. As the others have said, all things being equally matched, you would do suspension/wheels/tyres and brakes first before upgrading power. Exterior is completely up to the owner as to when to change it, again it depends on what they want to achieve.
Seems your mate is a bit of a sheep, being told to do things in an order, without using common sense to work out what acutally needs to be done