For amps i recommend the Schiit Heresy, JDS Labs Atom, or the Monolith Liquid Spark. All three amps offer more than enough power for the vast majority of headphones you could throw at them. They all can also act as a pre-amp for active speakers, and have low output impedance, so they can be used with sensitive IEM's without distortion. All amps are so capable that you can't go wrong no matter what you choose. The biggest feature difference is that the Atom has an additional input as a 3.5mm jack and the other two do not, though it has the worst build quality.
For DAC's my recommendation goes to the Topping E30, or the S.M.S.L Sanskrit 10th MK II as they both measure fantastically with excellent sound and offer very good features. Some alternatives are the JDS Atom DAC, or the Schiit modi, both of which aesthetically match perfectly with their respective brand amps, while still offering excellent performance, though less features than the other two amps. Again there are no bad choices here, so go with what features fits your needs, or looks the coolest and you will be fine.
You can also go with a DAC/Amp combo for simplicity. The Topping DX3 Pro is a fantastic option that offers a lot of quality features such as Bluetooth. Thought it does have a higher output impedance so it isn't really suitable for IEM's, but is fantastic for higher impedance headphones. The FiiO K5 Pro is a solid alternative to the DX3. it offers less features, but it still offers enough performance and sound quality to handle almost anything you throw at it, while being very inexpensive. It likely represents one of the best bang for the buck options in high end headphone audio.
The combo units will have slightly worse amps and DACs compared to the standalone units, however that won't really translate negatively in real world use, and they both are still exceptionally capable. All options provided here will be more than enough to handle DT 1770's and really most headphones on the market with no real issue, while offering great sound. You can pretty much use any amp listed, with any DAC listed, so just go for what features fit your needs, and don't stress the choice, as there really are no wrong answers here.
I will note, that I only covered more "budget" single ended options, because I believe beyond the price range these units fall into you get severely diminishing returns, with more expensive amps and DACs not necessarily sounding/performing better than these, but instead offering unique features that some may prefer. As well I did not cover balanced options, as the DT 1770's don't support balanced without heavy modification. Also, I don't view balanced output as something that offers much realistic benefit compared to unbalanced. That said I can go over some options if you want. Otherwise feel free to ask if you have any questions.