A nice looking case.
Specs say it supports 160mm air coolers.
I do not know where you shop or your prices.
Here is a noctua NH-U12s:
https://noctua.at/en/nh-u12s/specification
There is a black version which probably sells for more.
A less expensive cooler that I have used before is the scythe kotetsu.
Here is a review:
Weighing just over a pound and having only a single 120 mm fan, the Scythe Kotetsu still manages to compete and beat much of the larger competition. April 30, 2014 by Lawrence Lee Product Scythe Kotetsu CPU Cooler Manufacturer Scythe MSRP US$35 Scythe took a big step last year with the Mugen 4...
silentpcreview.com
Commonly available is the cm hyper 212.
That would work also, but I found it difficult to mount the cooler properly.
The instructions are not so good.