Problem Recording

I am using Audacity Version 2.1.1 on Windows 8.1
I am using a Logitech USB headset with microphone.

I belong to the Barbershop Quartet Singing Society and need to make recordings for learning purposes.
We are provided with a sound track with 3 parts prerecorded on it.
I am then required to record my part along with the other 3 parts to make the quartet 4 part sound.

I know how to import the sound track’
I have recorded just myself singing with the the microphone set to my USB microphone and the speakers set to my headset.
The recorded track has a very discernible hum before I start singing and continues throughout the recording.

I have also imported the track of the other 3 parts being sung and recorded just that track and it also has a hum on it.

What I want to be able to do is record my part along with the other 3 parts onto new track.

What I need to know is
1 what settings do I use for recording (headset or computer microphone and speakers)
2 what other settings do I have to set for recording?
3 what levels of volume are required when recording?

I would certainly appreciate some guidance on this matter.
I would hope I can record without the hum being present.

One of the instructions in the overdubbing sound-on-sound tutorial is make a straight recording. Full Stop. No overdubbing, no syncing, no barbershop quartet, no complexity. If you can’t make a straight, simple recording then you can ignore all the other instructions until you can.

I have a Logitech USB headset and it hums. I never figured out why and it probably doesn’t affect Skype or Games or other voice applications, but I can’t sing, make a theatrical presentation or record an AudioBook with it. The hum sound in the background would never make it past Quality Control.

So In My Opinion, you have a known microphone problem.

You can probably try to suppress it in post production by Nyquist Programming, notch filters, or Noise Reduction, but it’s never going to sound like you used a good quality microphone in a quiet room.

There were hum suppression filters posted and we can look.