Can you post a sample of the noise. PS, adobe audition has a far better noise reduction)
When using a USB mic, it is important to ensure that you do not use more gain than needed. If your focus is vocals only, then you want the mic to be within 1-2 inches of your mouth (about the same location where you would place a headset mic.
This will get rid of all or almost all of the noticeable noise, then if needed, a very light noise reduction can be applied, and you shouldn't be able to notice any loss of quality.
A moderately quiet PC is good enough if you have a cardioid mic, just make sure it is located in the opposite direction of the PC.
When setting up your levels, lower the gain to a very low level (far too low to be useful) then begin talking at a level where you can comfortably project your voice, then begin increasing the gain until your vocals hit -3dB on the levels monitor.
After that, you can you can apply multiband compression, and other audio processing in post, to keep the volume constant, and account for any variations from when you move your head a little.
The only time when noise reduction cannot be used, is if you are recording music. computers cannot differentiate noise from music.
PS it takes a lot of noise to begin impacting audio quality from noise reduction.
For example, here is a video I recorded for a Dom Bower photographer HDR challenge
In the audio, you will notice very little noise, even though my PC has 3 120MM fans running at full speed, and a top 140MM fan also running at full speed, with a 120mm fan on the heatsink at the time, also running at full speed, making for a very noisy system. (and I did not follow the rule of keeping the mic very close and the gain down, due to the mics size)
and here is a video with a similar mic setup, but with no noise reduction (couldn't use it because I was doing a quick video to show the sound leakage of a pair of headphones) (skip to 27 seconds)