I used a variety of cars to complete the drift zones - Alfa 4C, Subaru 22B barn find, BMW M6 FE, Hoonigan Focus RS - find something you find easy to control. upgrade as you would for most cars - reduce weight, add power, improve handling. In a move that will likely upset most in the drift lounge I found AWD much easier to use to begin with, though RWD has the potential to do better if I could just learn to control it more. For a beginner, go AWD so you aren’t spinning out so much.
I do have the Drift pack cars, but maybe because my first attempt was using a 1000+HP RWD in the snow with traction control off I spent my time going round in circles or off into trees. Hence opting for a more normal car, AWD conversion and something in the region of 500-800HP. Not enough power and you struggle to break traction for long enough. Too much and you are prone to spinning out or burnouts. With practice you can advance to more powerful cars or learn to control RWD instead of AWD. I can now get much greater angle on drifts in a RWD, but find it harder to produce that consistently without losing the back end.
Simplest drifts are e-brake. Build up speed down a straight, turn + e-brake to lock the back end, then power through to turn it into a slide. It takes practice to learn how early to start the turn in based on your speed and how to control the throttle. Steer into the drift to keep the car headed where you want it, while feathering the throttle (and some normal brake) to control the angle of the back end. If it is slipping too far round ease off the throttle or apply a little brake. Not enough angle try more throttle and adjust steering.
Drifting can also be induced by shifting the weight balance in the car. Applying the regular brakes shifts the balance of weight forward, giving more grip to the front wheels assisting with turn in, while reducing downforce on the rear wheels making it easier to break traction by applying throttle.
Some cars have such great balance you can initiate drifts just by turning on a straight road. The Hoonigan Focus is AWD but is incredibly responsive to turns and has plenty of power to break traction at will. You can have that drifting S bends down a straight road at will by timing your turns and throttle.
Traction Control actively fights your ability to drift. It detects wheelspin as a bad thing so reduces power to the wheels until you regain traction. This ends drifts earlier, reduces your speed and limits what scores you can achieve. Learn to drift with traction control disabled and you will be able to get much better scores. You will then control the traction of your car through a mixture of throttle control and angle of the car through the corners.
I probably did drift events in the wrong order - I managed to 3* all drift zones before I even went to the Drift Club series. With hindsight I would do them in the opposite order - Drift Club challenges first, then the drift zones. Drift club is much more forgiving and gives you more guidance as well as opportunities to practice that don’t result in failed attempts. Those cars have had a lot more tweaking done in settings, but as a beginner I wouldn’t advise messing around with that until you know your camber from your toe in.
Lastly for drift zones know that the scoring zone starts at the first set of flags - you can already be drifting through the start gates to be scoring immediately, rather than waiting until you are inside. Also some events are much easier in one direction, while others are perfectly achievable in either direction.