Basically and popularly, there are 2 types of potentiometers: A-type and B-type.
A-type, or linear type: resistance portion of pot. is directly proportional to the rotation angle of the pointer. This type is used in any place when need linear, for example: equalizer/treble/bass adjustment in audio amplifiers.
B-type, or logirithm type: resistance portion and rotation angle have a logarithm relation. This type is used mainly in volume adjustment in audio amplifiers.
These types are shown in pot. values on packages, for example: 10kA, or 10kB, means pot of 10kiloohm of A-, or B-type.
In principle, we expect higher gain in any amplifier. But higher gain makes system become more unstable. 200x gain may be good enough for your project, and you can easily adjust its value at IC amplifier to get your best result.
For LM386, you should look for the datasheet from National Semiconductor, as this is the original manufacturer, and NS often provide very detailed information for application in their datasheet, as well as seperate application note for the IC.
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