I also tried to find the "bare minimum wireless" for RPi Zero W using buildroot so this Q&A came quite high on the search results. Eventhough the original answer was somewhat helpful, it's definitely not the best one so I though it would be worth sharing my own findings:
Using buildroot 2018.02.2
to clean you config. Then (make menuconfig and) select following from Target packages:
Hardware Handling -> Firmware -> rpi-wifi-firmware
Networking applications -> wpa_supplicant
Networking applications -> wpa_supplicant - Enable 80211 support
Everything else that's necessary should already be pre-selected.
Then at /etc/network/interfaces
iface wlan0 inet dhcp
pre-up wpa_supplicant -D nl80211 -i wlan0 -c /etc/wpa_supplicant.conf -B
post-down killall -q wpa_supplicant
and at /etc/wpa_supplicant.conf
and now we're still missing the secret ingredient: the wifi driver must be loaded before the networking init-scripts kick in. You could Enable WCHAR support (at Toolchain -menu) in order to have eudev as /dev management (at System configuration -menu) which would automatically handle the driver loading. Actually I recommend this if you're going to connect UBS devices to your RPi....
...but if not, edit /etc/inittab and modprobe brcmfmac yourself just before the rc scripts are ran:
# Load Wifi driver
# now run any rc scripts
UPDATE 21.03.2022. Using the latest buildroot from
git://git.buildroot.net/buildroot it seems that there are some changes:
rpi-wifi-firmware is renamed to
brcmfmac-sdio-firmware-rpi-wifi which can be found under
brcmfmac_sdio-firmware-rpi at Hardware Handling.
wpa_supplicant.conf doesn't seem to be valid nor necessary anymore (if it ever even was)
I also found that if the wifi is needed for access over SSH,
OpenSSH should be paired with
haveged for faster random generator initialization. Without it the boottime can be minutes!
To fully prepare the board for direct headless access and considering all above, I made an external buildroot library with rpi-wifi package which handles all the necessary configuring from wifi setup to SSH config:
rpi-wifi at my buildroot-externals repo