First you have to understand what exactly a CPU cooler is used for. A CPU cooler is made to cool the processor so that when the processor does calculations in the background it doesn't heat up to the point of over-heating and that's when the processor itself gets burnt. Fire and smoke soon follows if your Power Supply Unit (PSU) doesn't support Over-Heat or Over-Voltage protection and as a side warning, Never ever go cheap on your Power Supply because that can be a fatal mistake, always go with reputable brands that work like Thermaltake or Corsair.
Now back to the subject at hand, The way it functions is the CPU cooler works much like a large dog's hair or a house attic functions. It's sole purpose is mainly to ventilate heat from the processor to the exhaust case fans and out of the system itself so it's important to strategically set up your case fans in a way that it gets rid of heat fast. You definitely need to position the fans outward to push the heat out, Some people might point some inward to give it cool air but for me I don't do that because generally the air in your house believe it or not has impurities from dust to dog dander that can build up inside your case and eventually get inside your hardware. The last thing you want is dusty hardware that can bring performance to a grinding halt and also significantly reduce it's lifetime.
When choosing a case fan, You will want to get a case fan that fits your needs. If you prefer a really quiet computer than a brand like Noctua would work, If you want a computer with lots of airflow than you'll want to go with something like Corsair. The way you tell whether a case fan is truly slient is by looking at the Rotations Per Minute (RPM). The higher the RPM, the more airflow it moves. The lower the RPM, the less airflow it moves. Also you'll want to check the Noise Levels which are calculated by A-Weighted Decibels dB(A). The higher to dB(A), The more noise the fan it will generate. The lower the dB(A), The less noise it will generate.
Now hopefully this will help you better understand the importance of the CPU cooler and also some advice on selecting case fans. I can't stress the importance of choosing a good Power Supply, That's the most single-handed component that matters in your computer.