Circuit Choices for AmpIifier Input
The hum you are most likely hearing is 60Hz (or 50Hz depending on your location) from AC mains. Use proper shielding, grounding and filtering techniques to stop noise from entering the amplifier circuit. 

A great place to start would be to build a conductive enclosure for the circuit, that will block electric fields that might be amplified.

The hard part will be blocking magnetic fields, because no material can block them 100%, but magnetic fields diminish with the distance cubed, so removing the circuit from nearby sources can help.

Make sure there are no conducted emissions, meaning make sure your power supply is clean. Check it with an oscilloscope if possible and look for noise or ripple. If possible use a battery to power the circuit, if the hum goes away the power supply could be a likely source of noise. 

Breadboards are also terrible for developing circuits, solder the circuit on perfboard, or wirewrap it.