What fan would you recommend for the X4 860K?

The 860K is a 95W processor so a lot of low profiles might not be able to handle it. I'd probably look at something like the BeQuiet Shadow Rock 3 or the Coolermaster MasterAir G100M which are both rated for processors up to 130W.

If your system can fit it, I would recommend getting the AMD Wraith Max or possibly the Wraith Prism. There are plenty of people on Craigslist and offerup who are trying to sell their Wraith Prism coolers in order to recoup a bit of their costs.

The Wraith Prism is the stock cooler that comes with the Ryzen 7 2700x, 3700x, 3800x, and the Ryzen 9 3900x.

I have successfully put a Wraith Prism cooler on an older AM3+ motherboard and used it to cool an FX-8120 and FX-8350. So the only reason it won't work is because the chassis has poor airflow.

Other coolers I recommend are the Scythe Big Shuriken 3 and the Noctua NH-L9. Check those out to see if they'll work in your mini-ITX setup.

Other than that, the Athlon x4 840 is only good for old games, web-browsing, email, and tasks that don't need a lot of processing power. If you're doing anything hardcore with your system then maybe an upgrade is in order. The Athlon x4 840 is about on par with the old Phenom II x4 processors which were popular 10 years ago.

Cooler like the 212 Evo, Gamaax 400, etc are meant for mid tower cases.

just get a 212 evo. its the most popular. but fm2 is old stuff. u really need to get a ryzen