High speed lane change[...]High speed lane change and emergency stop. In this case, I was required to change lane and stop in the shortest distance possible. Again, I knew the priority was to first brake, as the car (with ABS) would be more stable. If I had tried to change lane first, and then braked, I would have risked losing control unless I held off braking until the chassis had recovered from the lane change. The Boxster was highly impressive once again – once firmly on the brakes with the ABS operating, it was easy to change lane rapidly and without drama.
The priority is to brake first for other reasons, except outright stability. By braking, you slow down and "earn" more reaction time towards the steering manuever. The additional time can also be usefull for th obstruction (i.e. a driver crossing your path or oncoming towards you) to get out of your way.
When a driver needs to brake suddenly, it's always best to gently tilt the car towards the "open" side (the left shoulder on the motorway, e.g.) so your car is heading diagonally towards the obstacle, and very gradualy moving both out of the way of the obstruction and of more traffic coming up behind.
However, if a proper avoidance manuever is needed, besides this initial steering input, than it is best to first wipe off as much speed as possible (again, while gently "slipping" towards the desired side) and wait to the very end of the braking (just short of the obstacle) to make a second, more dramatic steering movement.