AFO is a step up from mid-fi headphones, and is more likely to show limitations in your DAC or amp than any cheaper headphones you may have had before. You may find with very well mastered tracks you know well, the music you are familiar with sounds worse than expected (certain instruments in quiet tracks sound shrill). There's details in the music that I could hear with the AFO, that I couldn't with the HD660S.
I wouldn't personally use any DAC/amp combo that goes less than $800 I'm using near high end headphones, even if somebody could successfully prove that my gear doesn't sound any better than something like a Chord Mojo, at less than half the cost. I had overcome the fear of paying too little. I don't even agree with some of the marketing that goes with my Gilmore Lite mk2, like "discrete output stages sound better than IC's". Not always. There's cost savings to be had in IC circuits that are well done, for lower power applications.
During critical listening, I always try to use gear that's more expensive than what I have at home, at the store, if I am in doubt about my DAC or amplifier's quality. Then I know where the problem is later if I find any. I do realize that not everybody can listen in person anymore.
Magni 3 and JDS Lab Atom? Don't expect much for $100-$120. I would only use them with low quality sources and 'phones that sell for $400 and under. There's lots of gear available at every price point: large and small, combined and separate. There's economies associated with using combination DAC/amp units like sharing the power supply, as separating things doesn't always give you better sound. Most of them have at least separate regulators for different parts of the circuit.