For calculating $V_{stall}$, why should be used $C_{L,max}$ and not $C_{L,min}$ (that would be more prudent)?
The stall speed is the speed at which you can still fly the plane in level flight. This is important, because strictly speaking, stall happens at a certain angle of attack, not at a certain speed. In other words, you can safely fly a plane way below stall speed - the problem is that you'll be doing it nose-down in order to keep the angle of attack to a minimum (and that as such you will quickly exceed the stall speed again - hey, we just did a stall recovery maneuver!)

So, let's see what happens when we approach stall speed from a higher speed, while flying level. As we slow down, we must increase our angle of attack to maintain level flight - this way, we are increasing the $C_L$ of the wing, as to keep the lift $L(=W)=\frac{1}{2}\rho VSC_L$ constant when reducing our $V$. Ideally, we'd like to keep increasing our $C_L$ as we reduce our $V$ - however, this means we keep increasing our AoA (angle of attack) until it gets past a critical point, where the airfoil stalls due to flow separation at the suction side of the airfoil.

So really, using $C_{L,min}$ would be nonsensical - if your wings would have a lift coefficient so low at such a low speed, I can guarantee you that $W&gt;L$, i.e., you plummet from the skies. We need to increase our $C_L$ to maintain level flight, and the stall speed is exactly the point where we can no longer increase our $C_L$, or in other words, we arrived exactly at $C_{L,max}$.