You can use the DAC on the pi itself; you will not be able to tell the audio quality difference on any equipment you own (your ears included).
There is a stereo mini jack audio output on the pi. Just use that and don't waste your money on audio woo.
(This is also a standing bet of $5000 to anyone who can pass an ABX in front of me to discern the difference between the two in headphones of their own choosing. You pay if you lose.)
Sorry, but I did try this, and it sounds absolutely awful. There's a ton of noise. I don't know if my Pis (and I've tried 3 of them) are different from yours, but a cheapo $20 USB sound adapter already has a much better noise floor than the built-in one. This is regardless of what I connect them to.
There's "audio woo" where you spend $1000 for a USB to SPDIF adapter that literally does almost nothing, and spending $50-100 for a decent DAC that doesn't have an audible hiss.
I've never heard the pi DAC... I wonder how good it is. I have some great headphones and great ears. But yeah I agree the built in DAC should be fine for what people seem to be using this for (playing music in a group setting, or while doing chores).
If you plug headphones into the Pi's minijack and turn the volume down to a comfortable listening level, the noise floor on the Pi DAC is very, very obvious. It sounds like hell. Try it yourself before you lose your $5000. :)
There is a stereo mini jack audio output on the pi. Just use that and don't waste your money on audio woo.
(This is also a standing bet of $5000 to anyone who can pass an ABX in front of me to discern the difference between the two in headphones of their own choosing. You pay if you lose.)