There are three issues at work here: the voltage ripple on the output, peak currents through the rectifier, and the reverse-recovery losses of the diodes. Within the context you specified (household) the latter two are unlikely to matter, but I'll include them anyway for completeness.
First, the ripple voltage. I=C dV/dt. If you know the current load (I), and you know how much ripple is acceptable for your application (dV), then you can extract a relationship between the capacitance (C) and the half-period of your AC line (dt). How much ripple is acceptable? Depends on the application. But for a fixed capacitor, higher frequencies will reduce the size of the ripple, and lower frequencies will increase it.
Second, peak currents. The rectifier doesn't conduct all the time; it only conducts when the AC wave is higher than the value of the DC capacitor. So your AC voltage looks like a sine wave, but the current being pulled looks like a big spike just at the peak of the wave.
Now, these spikes are sub-optimal. They don't look at all like a sine wave, so they cause harmonics on the AC line. And the RMS current of those spikes is much higher than a sine wave of equivalent power delivery would have, so they stress any fuses or breakers upstream.
Characterizing the current spike can get complicated, because it depends on the frequency of the AC, the capacitor, and the inductance of the AC line. The more the inductance, the wider-in-time and shorter-in-amplitude the pulses get. (For high-power three-phase applications it's common to add a big inductor to purposefully spread the diode conduction time and reduce all those problems, but I don't think it's common on household stuff. In general, people don't really care about harmonics in those contexts.) But unless you're pulling something close to the full rated power of the breaker, this won't be much of an issue.
Third, the diodes involved usually have a reverse-recovery time. When a diode goes from being forward-biased to being reverse-biased, it actually takes a finite time for it to stop conducting. (There are zero-recovery diodes, but they aren't usually used for 60 Hz work.) During that time, the diode acts like a short circuit, meaning it dissipates a lot of power. This time is typically on the order of microseconds, so for a 60 Hz line you don't see much additional loss, and can probably ignore recovery losses. If you were operating in kilohertz, you'd have to account for it.
Frequency matters, but not much for your stated context.