In you 200-250 Euro price range, most headphones can be driven easily enough with a phone etc. that you could enjoy it while waiting to replenish funds for an amp.
I enjoyed the DT770s while I had them, but why not go for something new and shiny like the Meze 99 Neo?
I second Meze 99 Neo! It is much better than ATH M40 in every possible way in my humble opinion... Much airer sound, much better separation and much better expressed, more impactful bass, cleaner midrange and smoother treble. In fact, the part with the smoother treble might not appeal to absolutely everyone, but it has better detail and can be solved with EQ.
I third the Meze. Excellent in a lot of ways, and a great price!