I understand that it should be some kind of preamp with a compressor and a bunch of different incomprehensible buttons and levers, which, from a mediocre sound, will make a firm one?

Recording a saxophone
freebears.com/keilwerth
is not much different from recording a voice ... Only you need to compress more, and almost the same thing ... There must be a microphone (good) with a sound card (external), everything else is done in the computer ...