AMD processors run cool. The FX 6300 is rated as a 95 W CPU. Doesn't have big power requirements. Even with reasonable overclocking, a 125W to 140W cooler should be be plenty. Almost any decent air cooler would work.
I can't really see any reason to go with water cooling or a massive 140 mm air cooling tower on an FX6300. If you needed that much heat dissipation for the CPU, other parts of your MB, like the VRMs with no heat sinks would be failing.
In a full size case with lots of clearance for height, the Noctua NH-U12S would be a high-end choice, with 140W+ capability. The EVO212, a good budget choice. Basically, any tower cooler with a 120mm PWM fan would be good.
If you have a smaller case or just to take up less room, the 92mm Noctua (NH-U9S) would work great with an FX 6300. That's rated at 125W, so you've got plenty of reserve over the stock FX 6300 95W rating. You might not be able to win overclocking contests, but you could certainly overclock the CPU to a reasonable degree at or near stock voltages and have plenty of cooling. It probably wouldn't be smart to start cranking up voltages for ultimate overclocking with your board and power supply anyway.
If you're not overclocking, any of those cooler would run really really cool and/or really, really quiet, even under torture test loads. With no overclocking, I would expect even the small 92mm fan Noctua to keep max CPU temps at or below 50C even with a Prime 95 torture test and still be much quieter than the stock fan (2000 rpm versus 3400 rpm the stock cooler).