I too am new to tubes, it's been about 4 months for me. I had a similar choice as you, I have a headphone system and a stereo system. I originally thought the D1 would be the best of both worlds, and purchased it to feed a Bob Latino tube amp and the built-in headphone amp for Sennheiser HD558 and Grado SR80i headphones.
Without boring you to death with the details, I ultimately was not happy with the entire system......it just felt "off", and I could not always put my finger on why. I tried a bunch of solutions, but ultimately help actually came from Ryan in tech support at Maverick. I will paste his response to me for my problem.
~~If that's the case, D2 is clearly the best DAC for you for the sake of the sound quality. Honestly, I am not a "believer" of upsampling, D2 is not an upsampling DAC, it sounds better than the D1 Plus which is an upsampling DAC. You will feel the music is more 3-dimensional and sound stage is wider if you compare the D2 to the D1 Plus. Also, you don't really need headphone amplifier, volume control and analog inputs on the D1 plus, as you are pairing the DAC with tube amplifier. By having less "features" will improve the sound quality as well.~~
So what I took from Maverick's response (and honesty) is that: The D1 has compromises in it because it is designed as a "Swiss army knife" product, and that it does many things well.....but nothing very well. To me that made sense, the D1 is designed as a DAC, up sampler, tube buffer, pre-amp, and headphone amp all in one unit....some compromises were made for the sake of price and size, and it shows up in the sound.
The D2 on the other hand is designed as a "no sacrifice for the money" DAC only unit. If it does not improve the sound and function of the D2, it is not in the unit. No pre-amp, no up sampler, no headphone amp....just superior components.
In the end Maverick swapped out my D1 for a D2 DAC and I matched it to a Schiit Magni headphone amp, and all I have to say is "holy *****". All of the previous problems were gone; detail, punch, clarity, openness, instrument placement, black background....all present. I really would recommend that you reach out to Maverick tech support, just to get their feedback. I've found them very helpful. Best of luck and I hope my experience can be helpful.