Matching with a Preamplifier
Resistance, capacitance, cables, oh my!
— How do I set capacitive and resistive loading for a Moving Magnet (MM) cartridge?
— There are a few "rules of thumb" that only apply to Moving Magnet and other high inductance cartriges (MI, fluxvalve, etc):

• The higher you go in resistive and capacitive loading, the "brighter" the sound is
• If the sound is too dull and lacks sparkle, increase resistive loading
• If the sound is too bright and tiring, decrease capacitive loading if possible. If not, decrease the resistive load
• No load adjustment is needed for modern MM-type cartridges (Ortofon OM/2M, Audio Technica VM, Sumiko and other Excel derivatives, Goldring). They are designed to be linear into a "standard" 47 kOhm/200 pF (picoFarad) load
• Typical tonearm cable has a 150-200 pF capacitance. Do not add more capacitive loading on the preamp side unless needed

Unlike the moving coil cartridges, there is no easy way to set the loading correctly. It will always be your subjective preference, unless you have a good test LP and a signal analyzer.

If you have the same recording on the LP and in digital format, and are happy with digital's tonal balance, you can try and match it by adjusting the loading. Digital releases are mastered differently, so there will never be an exact match.

Before the industry settled on today's typical 47 kOhm/200 pF loading, there existed considerable variation. In the 1970s, 75 kOhm loading was considered standard by some hi-fi manufacturers, and that's what the old Shures, Stantons and Pickerings might be expecting. If you have a vintage cartridge and it sounds dull, raise the resistive loading.

Many (but not all) 1970s, 80s and 90s Audio Technica cartridges are too bright into 47 kOhm. Loading them into 35 kOhm will result in a more linear response and a less fatiguing sound.

— How do I set capacitive and resistive loading for a Moving Coil (MC) cartridge?
— In general, setting the loading for the moving coil (MC) cartridge is a lot easier than doing the same for MM.

For impedance matching (resistive loading), start with the lowest available with your preamp or step-up transformer. Select a track you know well, with prominent highs and clean but full bass. Start increasing the loading, and listen to the track after each step.

Once you hear no difference in highs and bass with the increase in resistive loading, decrease it by one step and leave it there. That's it, you're done.
This method might not work for some MC cartridges. "High output" moving coils in particular need "standard" 47 kOhm loading.

— Why does capacitive and resistive loading of MM cartridge matter so much?
— The short answer: because of immense inductance of fixed coil cartridges (moving magnet, moving iron etc). 0.3 to 0.7 Henry is typical, more than 1 whole Henry is not unheard of. Paired with a huge inductance, even minuscule capacitances (50-200 pF) suddenly matter a lot.

— The long (but still somewhat simplified) answer:
Here is the electrical model of a typical fixed coil (MM/MI) cartridge, with inductance of 0.5 Henry and internal resistance of 1 kOhm. It is loaded into 200 picoFarad of capacitance and 47 kOhm of resistance.

The cartridge's inductance and the load capacitance form a resonant circuit. Because the coil inductance is so high, the resonance frequency $$f$$ is in the audible range. Depending on the cartridge, it can be as low as 12 kHz.

$$f={1\over{2\pi\sqrt{L_{cartridge}C_{load}}}}$$

The loading resistor $$R_{load}$$ is there to dampen the peak of this resonance. What would happen if we change its value?
The higher it is, the more pronounced the high frequency peak is. The curves above are shown for 200 picoFarad capacitive loading.

Changing the capacitive loading, we see that with higher capacitance, the peak becomes larger and lower in frequency. But also the subsequent high frequency roll-off becomes steeper. This is why, for subjective adjustment, it is better to change the loading resistance and not the capacitance. With resistance, only the HF peak amplitude changes. With capacitance, you change at once the peak frequency, amplitude, and high frequency roll-off.