I need suggestion about motors

I will design a robot hand. I need this hand to operate from 0 degree to 160 degree or a bit smaller or larger degrees. There will be only two state of the arm either in 0 degree or 160 degree. In other words, I do not need to control within this range. Do servo motors have this control property? Or should I use stepper motor.

Hobby servos seem a good match - but it depends how much force and rigidity
you require. Is this hand needing to lift and manipulate or just move itself?

Friend. The question I am asking is whether I can arrange the operation angle from 0 to 150-160 or not. Wherever I read about servo motor it is written that it can be cotrolled within 0 and 180 degrees. It is not written that for example, it is possible to operate arbitrarly with such angles 0,30,45,60,...160,170,180. I wonder this issue. In other words, What is step size in the range between 0 to 180 degrees.

Servo.write takes a number in degrees, so your minimum step size is a single degree. writemicroseconds gives you more granularity than that. Whether your particular servo can react to that granularity is another question of course but it should come close. Another question is the range it has - not all servos can do 0-180. It may be more like 0-160 (or less). Sadly, the vendor websites rarely seem to publish this information.

hydrv:
The question I am asking is whether I can arrange the operation angle from 0 to 150-160 or not

You can move a servo to any position within its range of travel. It would be up to you to choose a servo which provides a sufficient range of travel, and operating speed, and force, for your application.