I found that the stock cooler is loud and inefficient. The problems arise in the summer with the stock cooler if you have a hot room
like me. So i would go with an aftermarket cooler even if you go and choose the non K version.
I bought the CNP9900 (because it was OVER 9000
)) with the 3570k, overclocked it to 4,2Ghz and i'm getting around 60 degrees celsius on prime95. It is not the quietest cooler out there but it certainly is better than the stock one and i'm getting great performance while it suits my case and blue lights.
In your case i would go with the K version since it is almost the same price and the Arctic Cooling Freezer 13.