help cooling oc 3800x

[Ruboka]

Hey,

I am building a pc for a friend.
The specs are:

ram:patriot viper blackout 32gb cl16 3200mhz)

ssd: samsung evo plus 1tb nvme 

case: coolermaster nr600 with odd bay for blu ray disc drive

mb: msi b550 a pro (still cheap but good b550 mb)

cpu:ryzen 7 3800x

gpu:  ZOTAC Gaming GEFORCE RTX 3060 Ti Twin Edge OC

Psu: corsair tx 750m if its enough for oc(some confirmation maybe?)

 

Now the cpu cooler:
 

Would be the NH u 12s enough or what cooler should  I go with?

The 3800x will be overclocked with 1usmus clocktuner for ryzen about which Linus did a video.

 

Like would be a dark rock 4(non pro) enough? (would also appreciate some help regarding ram clearance for the dark rock 4)

I dont know many good coolers.
The nh u 14s would be the next I know, but the case has 166mm clearance and the 14s ist just 1mm short from max. Would this work? How reliable are those numbers?

 

Thanks in advance for the help

Update:

Going to get a ARO-M14 based on @WoodenMarkers suggestion in the Cooler Tier List Thread.