Control Spotify with Media Keys
If you use the Spotify desktop app, the media keys on OS X work by default (sometimes iTunes randomly "retains" the keys: just reboot). For the best results, don't keep iTunes and Spotify open at the same time.
If you use the Spotify Web Player, you can enable the media keys using BeardedSpice, a free application which enables you to control web-based media players using you keyboard media keys. It also works for YouTube, for example.
If nothing helps to make Spotify take over the keys, check if you have Google Music installed in Chrome apps, because it always takes over these keys. Removing the Chrome app immediately makes media keys to work in Spotify.
I've found this helper application : Magic Keys ; Graciously written in a generic way by the creator of the Gear music player.
iTunes still sometimes pops us when using a Bluetooth control however, but it's minimal and non-intrusive and works well otherwise.
You can go into System Preference - Users&Groups - Login Items, then disable iTune and Spotify at startup, restart, then start Spotify which triggers Spotify helper to take priority control of the media keys ... Good luck !!!