No need to start the car as you want to stabilize the booster pressure.
Funny enough i learned in college to follow the service manuals according to the brake proportioner.
Which usually was closest then the furthest away on the same lines of the proportioner.
Basically it will help stabilize pressure if the car breaks a brake hose by losing only 2 wheels instead of all 4 in the case of a leak. It usually keeps the front left and rear right as one channel and the other 2 as the other pair.
I always started at the closest to the master cylinder as to remove as much old fluid as possible eaiest before pump new fluid throught the lines.
So basically the driver left ,then rear right ,then front right and rear left.