Hi Björn,
I don’t have in mind a specific model. I believe that most modern models will work fine.
I have seen openHAB2 running on NAS boxes from 2 manufacturers: QNAP & Synology
Synology related stuff:
http://docs.openhab.org/installation/synology.html & Synology DiskStation
QNAP:
http://docs.openhab.org/installation/qnap.html & openHAB installation on QNAP
there are more threads in the forum with support for these 2 platforms.