Here’s a tip I got from Zero (thanks!). There’s a new device called Gramafon, and it does exactly what my solution does, but it works out of the box, for 59 euro’s. It’s a small device which you can connect to your internet, and to your AV receiver or wireless speakers. After that you can connect to the device from any other device with Spotify Connect. It has a build-in DAC, I don’t know if it’s a good one, but I think it probably is.
So this is a very nice solution if you want something which works out of the box, no setup or installing of applications. If you want something more do-it-yourself or you want a device which you use for more things than Spotify only, than a Android Mini PC, optional with external USB DAC, is your best solution.