To demonstrate an elastic collision, a teacher places a tennis ball on the floor. she wants to hit the ball so that the following conditions are satisfied. 1. after collision, the tennis ball should roll with the velocity of the ball that hit it 2. at the instant of collision, the ball that hit the tennis ball should stop. what ball should she use? golf ball, tennis ball, basketball, or bowling ball?

Those conditions are met when you have an elastic collision of equal masses. 
So the answer would be a tennis ball. 
Let us write momentum conservation law for this problem. The left-hand side is before the collision and right-hand side is after the collision:
 
What this equation means is that all momentum of the first ball is transferred to the second ball and velocities before and after the collision are the same.
There is no need to write energy conservation law. We can see that above equation holds true only if .