I've been playing MMOs on consoles since FFXI and my absolute favorite keyboard, by far, has been this Logitech K480. Excellent response with the PS4; Bluetooth with actual range; compact; Can pair 3 different devices simultaneously; battery life is fantastic (had mine over a year and still on the same set.)

https://www.amazon.com/Logitech-Bluetooth-Multi-Device-Smartphones-920-006342/dp/B00MUTWLW4/ref=sr_1_1?ie=UTF8&qid=1476153204&sr=8-1&keywords=logitech+k480

Logitech K480 would be better, no?

This Logitech Keyboard has been working great for me. I like that it works with both iOS and Android. I've paired it with my Android Phone, Amazon Fire Cube and my iPad. Set up each device once and you can turn a knob to select the one you want to use.

Works great!