maybe this question isn't really related to FHEM, but anyhow good questions. And question in return: why did you move away from the RPi? If it is for FHEM only, this is to me the by far best HW choice, as it has enough CPU punch for the task (at least RPi2&3) and very low energy consumption.
Which Linux to use? This question seems to be as old as Linux itself and largely depends on how experienced you are with Linux and how much stability you want
Debian: focus on stability, but many SW packages in older versions
Ubuntu: based on Debian but has newer SW packages
Linux Mint: based on Ubuntu with always the newest SW (hence probe to be less stable)
Slackware etc.: to experienced Linux users who focus on small kernel footprint.
I would think Ubuntu Server 16.04 (LTS) is by far the best choice. It has long term supprt, a huge selection of SW and by far the biggest community out there for help.
Which leads to the second point WLAN: with 16.04, the way (W)LAN works has slightly changed. So the typical way of modifying /etc/network/interfaces isn't the recommended one. Best starting point might be to search the web for Raspian WLAN and pick very new search results.
Side note: the WLAN driver is working?