Either are okay. Ethernet isn’t going to be a bottleneck; a hi-res album wil take around 10s to transfer in its entirety, so streaming realtime will have no impact and I see no disernable difference between a local drive or file share.
That said, I have a 1TB Trascend StoreJet connected to the NUC USB3 interface for media. For compatability use exFAT. There is no need for a fast HDD. Some use ann SSD since the NUC is in their listening room.