is the stock cooler good enough? or buying new cooler will be a good option? won't overclock.It's not really irrelevant.
9600k looks expensive for what it offers at 6 cores/6 threads and doesn't come with a cooler, whereas the 3600 gets you 6 cores/12 threads and does come with a cooler.
The AMD stock cooler is fine with it:is the stock cooler good enough? or buying new cooler will be a good option? won't overclock.