Try using something like a P&N Countersink drill bit first (available at Bunnings). They are adjustable and then set the torque on your driver at a lower level. - JDE
P&N Quickbits certainly appear to be a great way to get a perfect countersunk hole. Although it doesn't come with a drill bit and is a two-step system I've been using a P&N 13mm Rosehead Countersink Bit which I have found to be very effective. It still requires you to keep the bit perpendicular to the surface and you'll want to be careful that you don't go too deep.
If you are just using a normal drill bit any of the above-mentioned products will make your life a lot easier. - MitchellMc
If you are having trouble with depth I would stick with the P&N Quickbits. - r23on
I have a set of countersinks with pilot drills and a vix bit for hinges. I prefer screws with either square or hex heads so they won't slip like philips heads may and bits with some length so you can get the screws straighter for driving. - Brad