Most stable ROM?

May be the wrong place to post this, my apologies if so.

I've just purchased a Nexus player. I have also got an air mouse/keyboard combo as a remote (best I've ever spent). I only plan to use a few apps on the device:
- net flix
- kodi
- youtube
- general web browser
- maybe songza

and I'm wondering which ROM might be the most stable? I've heard of people having issues with Netflix off stock, on stock, yes, no, maybe... mine is currently running stock, v5.1.1. Which one is the most stable from my usage point would you fine people say?

Stock 5.1
Stock 6
AOSP
Lollirock 5.1
Lollirock 6


Thanks so much!