iPhone to NAD 316

At least go with airplay so you got some freedom. It can't dound sny worse

If the amp can connect by airplay that’s good - it’s red book 16/44 quality, so the same as connecting a CDP and more than you can get from vinyl. 
If you think you can hear the benefits of 24/96 you will need the Apple Camera Connection Kit. Some say (like Audioquest) the powered version of the CCK sounds better than the unpowered.  But either CCK will give you a good feed to a DAC and will bypass the one in your phone. 

What are you playing from your iPhone?  If its lower-quality files like MP3 or Spotify, your Lightning to RCA will probably be fine.  If you have CD or higher res quality files, you might consider an inexpensive DAC, like the AudioQuest Dragonfly Black ($99).  You will also need to get a Lightning to Camera adapter (to plug in the DAC), and then 3.5mm to RCA adapter.  The Dragonfly will be a noticeable improvement over the iPhone DAC.  Apple sells two different camera adapters.  Get the one with the additional Lightning socket so you can charge your phone while listening to music.

Whatever I do, I’m not especially concerned with audio quality. I wouldn’t be using my phone as a source if I was. 
I’m not familiar with AirPlay. But I assume it will involve hooking up some sort of signal receiver at the amp end of the equation. NAD doesn’t have any sort of apple-ready technology in it, does it?
Dinosore, I feel like I should have the name. Is “Luddite” taken? So you’re saying that the iPhone to RCA will work? It was my understanding that when Apple used the old style headphone socket, the phone put out analog content. But when they switched to the lightening port, they got rid of the DAC and started putting out digital content. The DAC is now in earbuds or EarPods or whatever they’re called. So it seems like I would need a DAC somewhere in the loop. Not for sound quality but just in order for the music to play. 
I can risk the $15 for the lightening to RCA and, if it doesn’t work, it’s not the end of the world. But should I buy some kind of AirPlay receiver instead. Audio is fraught with so many pitfalls!

Just get a lightning to rca adaptor for 12 bucks and call it good. It will output analog you don’t need an external dac if it’s just a convienience hookup and sound quality is jot a big deal.