Headphone DAC for under $150.


I am a high school violinist looking to assemble a budget mid-fi system. I currently have a Primephonic subscription on an iPad (so plenty of lossless music available) and Sennheiser HD569 headphones. Because of the low impedance of the HD569s, I don’t think that I need an amp/preamp.
I have initially narrowed my options down to these three DACs (in no particular order):

1. FiiO Q1 Mark II 
2. Schiit modi 3
3. iFi Nano iDSD Black Label

(As far as I know, all three DACs have USB inputs that are compatible with both iOS devices and PCs.)
So here are my questions:
1. The iFi is almost twice the price of the other two; is buying one used a significant upgrade over a new $99 DAC?
2. Is there any sound quality difference between the FiiO and the Schiit? Right now I don’t have access to any DSD files, so is it better to buy a PCM-only DAC?
3. I have read on several other threads about the Apple Lighting Camera adapter. Would I need to purchase that in addition to any of these DACs? (My understanding is that the FiiO comes with a specific Lighting to micro USB cable.)
4. If there is something that I’m missing (either a product or a concept) I would appreciate it if you would let me know. 

Thanks for your time and knowledge!
Hey! I'm a big fan of Fiio headphone amps. If it's your cheaper option and you can't hear both with your headphones, jump on it. 

The Fiio Q1 includes a Lightning (not lighting) to USB adapter built in! 

I know it's not popular among audiophiles, but the latest Bluetooth/Aptx DAC's are really convenient for commuting. 
Oh, one other possible suggestion you might be interested in is the miniDSP headphone amps.

What they add is the ability to EQ to adjust for your headphones and personal taste. One way you could use this might be to help you listen to different aspects of a recording.
Go with the Schiit Modi 3. That one sounds fantastic. Huge soundstage.

Otherwise I like Topping D10 or D30 in that price range
+1 for Schiit Modi. I own the Modi 2. It has USB input only. No external power supply.