Hi,
Those DT770's are not really appropriate for content creation, they're a "V" pattern response with heavy mid bass and bright treble. Mixing with that you will end up with a result that someone else will listen to, if you made it neutral, as having lower bass and lower treble. You may want to EQ them to be as neutral as possible, or get significantly more neutral headphones for content creation.
Driving the DT770 250ohm doesn't take much, but yes typical onboard OPamps on a motherboard may not have enough output for whatever SPL you're wanting to listen at comfortably.
Also, typically for content creation you would want something other than just a headphone amp. Typically you would want audio interface that has several options for analog and/or digital inputs from mics, midi, etc, as well as real time headphone monitoring, so that you can manage the mixing of instruments. Obviously this is not needed if you're strictly doing digital content creation on a DAW with a keyboard and headphones.
If you just want a decent desktop based DAC/AMP that has good quality, plenty of power for any headphone you'll get, and isn't just cheap Chinese stuff you'd have to velcro to the desk to not lose, check out the
Schiit Fulla.
Very best,
