Disc brake/drum brake refer to some of the hardware that you can probably see behind the wheels. Disc is definitely better -- smoother, more controllable, cools down faster, easier to service...
The others refer to the electronic control of your brakes. ABS was the first such system. It prevents the driver from putting too much pressure on the brakes in a panic situation (or just very slippery conditions unfamiliar to the driver). Too much pressure will cause the wheels to lock up (stop turning too earlier) and lose steering capability or stability.
TCS (Traction Control System) is the natural follow up of ABS. It prevents the driver from putting too much engine power to the wheels causing the wheels to spin and the vehicle to lose steerability and/or stability. TCS does that by lowering the engine power from what the driver has commanded, and by automatically activating the brakes for the driver to stop the wheel spin.
ESC (Electronic Stability Control) comes in many different names between manufacturers, and is being standardized and required for US and other countries. Unlike ABS or TCS, which will only trigger if the driver brakes or accelerates too hard, ESC can activate the brakes automatically when the car gets out of control even if the driver wasn't braking or accelerating. It does that by braking one of more wheels independently (not all 4 at the same time) to cause the vehicle to turn in the direction that the driver is steering - with the right amount. It will also work if the driver is braking or accelerating - controlling the engine power at the same time.
Notice, all three of them work only when the car is in trouble. Most people rarely get into the kind of trouble that require these systems. However, when you do, they could become the difference between an accident and not an accident. So you can kind of look at them as insurance. However, in places when it snows and gets cold a lot, I would highly recommend them. In those conditions, a lot of people simply mis-judge the car's capability and drive very close to the limit of adhesion all the time without knowing it. So people need these systems more than they think.
If you're buying a FWD (front wheel drive) car, and have a couple cars to pick from, and the only difference is one has TCS the other doesn't, then I would say maybe you don't need TCS. Most other cases, I would recommend it.