Arduino inside an electric guitar

You described some form of buffer/boost, some filtering (often integrated in existing designs) and a compressor.

There are lots of resources about guitar effects in a big diy guitar pedal building community, if you want to go the analog way.

Some of the bigger forums:

Projects are often available as kits.

For the digital route: Both, teensy with or without audio board or guitar pedal adapter and arduino pedalshield, will introduce noise into the signal chain (adc/dac, sampling frequency, interferrance, ...). Those platforms were simply not developed as audio processors. The teensy audio library helps offloading the necessary timing and conversions and has a wide variety of effects implemented, if you want to use the arduino environment.