I listen to rap, funk and pop. Right now I use my speakers and sometimes my Logitech G933. I want to move my speakers to the living room, so I have more space at my PC setup.If you need a closed back headphone for isolation it's a good choice. The 770 is often used in studios for monitoring. It's a V shaped signature with good bass, actual sub-bass and boosted highs. It's what I would call a 'fun' tuning vs a neutral tuning. Closed back headphones don't let in air so they can get hot after a while.
An open back headphone will give more soundstage and spaciousness. What kind of music do you like?
I use the Asus Rog z390-FIf you have a recent motherboard past the junk quality ones, you are likely to have a good enough audio chip on it to use without getting an external DAC for lower ohm headphones. For the $100 plus that DAC costs you should put the money towards the headphones first, or simply buy a second different pair to listen to.
Yea you don't really need an external DAC for that. Get the 770 set and grab a Phillips Fidelio X2HR which is a good accurate open set for the same price as the DAC you were looking at, which would be a nice contrast to the DT 770. Then you can swap around between them for different sound as you feel like it. You will have two good headphones but with different sound signatures and both will be very different sounding from the Logitech set you have. Then you can show off to your friends how many headphones you have LOLI use the Asus Rog z390-F