Okay, I'll just condense and simplify.
There is ALWAYS noise everywhere - except, perhaps, in an anechoic chamber. What you must do is "control" the noise. This is extremely difficult outdoors. It is easier to control noise indoors, but most low/no/mini/micro budget indie filmmakers never bother.
The "secret" to quality production sound is skills/technique and knowledge.
You will need to properly gain-stage your audio recording system. Improper gain-staging will increase the self-noise of the equipment being used.
The mic(s) must be as close to the sound source as possible and properly aimed - in the case of actors the mic should be in front of and above the talent (out of the frame) and aimed at the notch at the base of the throat.
Do everything possible to control noise on the set.
As stated previously this is quite hard to do outdoors, so the proximity and the aiming of the mic becomes even more important.
Indoors you have more options to control the sonic environment. Most indoor indie "sets" are residences rather than an actual film set. Unplug from the electrical outlet every electronic device that you can. Why unplug from the wall? When turned off most modern electronic devices (computers, TVs, cable boxes, clock-radios, microwave ovens, etc.), are actually in a standby mode, and in standby mode these devices still emit electric impulses into the environment. (Here's a "trick" that many low/no/mini/micro budget indie PSM/Boom-Ops use; put your car keys in the refrigerator so you remember to plug it back in when the shoot is complete.) Oh, all wireless devices - phones, pads, games, etc. - should also be turned off as they (obviously) emit all kinds of EM frequencies, preferably the batteries removed for the reasons previously stated.
To minimize the hollow, echoey, roomy sound prevalent in most indie films use lots of carpeting, sound blankets, heavy plush furniture and anything else that will absorb sound and reduce acoustic "bounce." You should also stay as far back from walls as possible, and try not to shoot directly at a flat wall to reduce standing waves.
After all of this there will still be noise. As APE mentioned the more advanced (i.e. expensive) the NR system being used the better the results. Also keep in mind in a budgeted professional audio post all that's left of the production sound are the lines of dialog; all of the spaces between are replaced with room tone.
I would suggest that you read a number of books about production sound and audio post, and spend some time at FilmSound.org or JWSoundGroup.net.