Noctua maintains a list of suitable coolers for different processors.
Here is the list for the 14600K:
Series: Raptor Lake-S, Socket: LGA1700
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Look at the specs for any cooler you are interested in.
Match that to the height available in your case.
160mm would allow you to use a NH-D15s which fits your budget.
The only stronger cooler might be the NH-D15 @165mm and some considerations if you have tall ram heat spreaders.
What is the make/model of your motherboard?
In unusual situations, there may be some incompatibilities.
Some motherboards place the pcie x16 slot too close to the cpu socket and can cause interference with some coolers.
Some motherboards have vrm coolers that are too large and will impact big air coolers.
Check the noctua motherboard compatibility charts:
Our motherboard compatibility list shows which Noctua CPU coolers are compatible with which motherboards. We indicate if optional mounting upgrade kits are required and if there are any restrictions such as when the heatsink overhangs the top PCIe x16 slot. Please use the filters and search...
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Noctua makes coolers that are both quiet and efficient.
You can pay lot's less but it will cost you either quiet or efficiency.