Amps aren’t *that* different in the sound department!
At least, ideally
At the core, you want a headphone amp that has enough output power for your device and a low output impedence. All while adding as little distortion as possible to the signal.
If you have all those things…the biggest differences between amps are features/ports/etc.
Most amps beyond the very cheapest ones will have the right ratings to power the 250 ohm DT770’s. I’ve used and enjoyed them with a Soundblaster X G5 and a Schiit Fulla, primarily. Although I’ve owned a handful of amps and DAC/amp combos during my headphone journey, I’m not a “closet full of amps” guy. There’s lots of other reviewers out there that provide measurements and closer looks at featuresets if you want to get in the weeds with that stuff.
If you’re looking at the difference between solid state and tube amps…solid state amps tend to go for accurate, clinical reproduction of the signal and tube amps add a little warmth to the sound, which solid state fans will deride as distortion.
There’s no right answer to this outside your own personal tastes.
I’d start with a commonly recommended cheap buy like the Fiio E10k, and carry on from there if you feel like you need more.
If you listen to the DT770 properly amped and still don’t feel like it’s doing anything for you, it might just be that you don’t like how it sounds. And that’s okay too. That happens a lot more than people realize. Sound quality has a wide level of subjectivity/personal taste to it. You can always play with EQ or just try a different pair at that point.