Relating transfer functions with step responses
In the given example you have 3 types of systems:


the ideal integrator (D) with a step response that grows infinitely (fig. 1); that's the obvious one, as you've found out by yourself.
underdamped systems with complex conjugate poles (A, B, and C): their step response oscillates
critically damped systems with a double real pole (E and F): no oscillation in the step response


So systems A, B, and C must correspond to figures 2, 4, and 5, whereas systems E and F must correspond to figures 3 and 6. You had already arrived at that conclusion.

But we have more cues. Clearly, system C has less damping than systems A and B, which have the same damping. Smaller damping corresponds to more oscillation (i.e. higher overshoot and undershoot). So we can conclude that system C corresponds to figure 4. The difference between systems A and B can be seen by using the Initial Value Theorem:

$$f(0^+)=\lim_{s\rightarrow \infty}sF(s)\tag{1}$$

For system A we get

$$g_A(0^+)=1$$

whereas for system B we have

$$g_B(0^+)=-1$$

These are the values of the impulse responses, i.e., the derivatives of the step response. We see that the step response in figure 5 has a negative derivative at $t=0^+$, from which we can conclude that it corresponds to system B. Then we're left with figure 2 for system A.

The difference between systems E and F is the distance of the double pole from the imaginary axis. The further away from the imaginary axis, the faster will the impulse response decay, and consequently, the faster will the step response rise. So system E must correspond to figure 6, and system F corresponds to figure 3.