In switching power supplies, the output capacitor is usually chosen based on the ESR, not so much capacitance, unless you are using ceramics.
For electrolytics, the ESR will dominate the output ripple.
Usually, you choose the cap such that its ESR is :
ESR< Voutripple/Iinductorripple,
where Voutripple is usually 50mV.
The contribution of the capacitance to output voltage ripple is usually negligible compared to that of the ESR.
As simple as that. The inductor current ripple is that expected at the highest output current and you set it in the first stages of the design, when you decide the value of the inductor. Note that the inductor value changes with output current, so it is important to calculate the current ripple for the worst case (for a buck, maximum input voltage, maximum output current, lowest inductance-due to tolerance and current dependency).
The capacitor is then selected for the required ESR. Then you check that the value of the capacitor is not outside the recommended limits. Otherwise you select another type, or parallel more caps, etc. Generally you can parallel two or more caps if you require much lower ESR than a single cap can provide. Note also that higher voltage caps have lower ESR. Thus, it is possible to choose a lower capacitance part, with a higher voltage rating and a lower ESR, possibly in the same package.
While you are at it, make sure you check the cap's current ripple rating and design life. The ripple current is:
Icaprms=Iindripple/√12
Make sure the cap rating is higher than the ripple. Usually this condition is very easily met, but it's good practice to always check.
As for design life, it is usually 5 years. Choose a cap based on its rating at the maximum temperature (85C or 105C, 2000 hrs. or more). Then for every 10C lower than the rating, the life of the cap doubles. Thus, for a maximum ambient (inside the P/S) of 65C, a cap rated for 3000hrs at 105C, will have a life of
3000*2^((105-65)/10)=48000 hrs. That is over 5 years.
The filter corner frequency is important for voltage-mode controllers. Current-mode ones do not "see" the inductor, nor the filter's double pole. Compensating the loop of a voltage-mode controller must take into accoutnt this double-pole.