The Noctua cooler is included because it is a good quiet cooler. You can set the fan speed at either 900, 1100 or 1300RPM, maximum noise level of 19dBA.
The cooler on the Gigabyte 7770 is pretty good as well. If you're willing to spend more on the build overall then this is the area where the money should go, aim for a 7850.
You can set the speed of the fans in the Antec Three Hundred Two, so those should be fairly quiet on the lowest setting. The fans which comes with the Three Hundred Two are:
140mm TwoCool: 800/1200RPM, 21.8/26dBA,
120mm TwoCool: 600/1200RPM, 17/23.7dBA.
The 13.5cm fan in the Antec HCG-520 has been measured varying between 500-1800RPM. It stays quiet below about a 300W load, which you shouldn't meet with a build with a 7770.
Alternatively, you could get an Intel i3 (less power hungry on load and should be less hot, therefore easier to keep quiet) and H77 motherboard: