So yes, if you’re sure about your Yamaha AG03 able to provide 120 Ω impedance for the headphone output, then the best choice is a headphone model with 250 Ω to avoid distortion.
The counterpart might be lower volume in your headphones but that shouldn’t be an issue if the specs of your card are correct.
There’s no need to go higher than this and it would require an amplifier to drive 600 Ω headphones.
All of that said, I would advice to ask Yamaha support about recommended headphones models for this interface.
If you’re not buying online and go to a music store, you can also take your interface with you and ask to demo different models, often solves many guessing & questions and avoids bad surprises.