Although I agree 100% that good tyres are a must as is suspension condition and on normal cars standard brakes in tip top condition are plenty good enough. Cars like the 3000GT/GTO for instance have a decent brake set up, which in good condition is suffice for road use with stock performance, when you start asking them to pull up a modified motor, they fall short of expectancy.
I uprated my fronts to 355mm discs with six pot calipers, my originals were 297/4 pot. Mitsu themselves even uprated them to 320mm/4 pot after a couple of years.
I noticed the difference immediately and this was running on Goodyear Eagle F1 tyres, all brand new and always in top condition, pressures monitored etc.
I also uprated the rears, all lines and fluid.
There's many things to consider in braking too, obviously. Master cylinder power/clamping pressure at the discs and M/C condition too, along with fluid quality and condition.
You will only exert as much pressure to the calipers as your Master Cylinder can transfer, simple as that, pushing harder on the pedal when it has reached it's optimum exertion won't make a blind bit of difference. Releasing and re-applying will, hence over riding ABS or employing a similar system if your car is of the non ABS variety.
I was taught cadence braking at a very early stage in driving and skid pan training and have always employed this method, ABS or not, as I know what the car is doing by feel, therefore have a better impression in my mind of how well I'm stopping.
This all goes back to one of my favourite points, learn to drive correctly after passing your driving test and you will become acquainted with; a) better road positioning, b) far better roadcraft and vision in general and c) how to avoid dangers and how to improve your chances of getting out of them if the worst does happen.
You can never predict what someone else will do but education at an early age will give you a far better chance of reading it. It's a bit like experience brought forward.