I am building a 5F1 Champ-style amplifier and I am wondering about what value of capacitor to strap to the cathode resistor? I have seen suggestions of 22 uF and 25 uF and I am not sure what value I should use.
I assume you are talking about the Cathode Resistor Bypass Capacitor. The purpose of these resistors in any transistor or tube based amplifier is to allow AC signals to "bypass" the cathode resistor and go directly to ground.
This results in a higher gain due to no "local cathode feedback". Typically this capacitor just requires. \$Z_c << R_c \$.
If this capacitor is to small, it will create a low cut filter, and remove frequency below a certain point. This is often unwanted behavior, but occasionally this effect is used for tone shaping, especially in some lead channels of guitar amplifiers.
For Tube amplifiers like this you will commonly see values of 22u to 100u.