Small headphone system

At your budget I’d definitely buy a better DAC along with the amp.  I’d very highly recommend this amp from Singxer that I use with my Hifiman Arya Stealth ‘phones and it just does everything right, is fully balanced, and runs in Class A for very refined yet detailed sound.  It sounds best in “Low Z” mode and with the power switches on the bottom switched to low output, which is likely all you’ll need for your headphones. 
https://www.amazon.com/Singxer-Balanced-Discrete-Single-Ended-Amplifier/dp/B08QMDM631/ref=sr_1_1?crid=204K2NV4Y44L3&dib=eyJ2IjoiMSJ9.4_l4LmYs2rQL_0rPnG1DxnqoK94ArDWt3DfhJmBV6Ghp8NqVE1ro_-q3DBeE2ua5.6OIKAdkfi9n8Xl1-VZlpL5rcvu8ityhl8OPuTCd46es&dib_tag=se&keywords=singxer+sa-1&qid=1724097507&sprefix=Singxer%2Caps%2C89&sr=8-1&ufe=app_do%3Aamzn1.fos.2b70bf2b-6730-4ccf-ab97-eb60747b8daf

For a DAC I’d recommend this Musician Draco that’s fully balanced and very similar to the pricier Pegasus that I use with the Singxer amp with excellent results.  The Schiit Bifrost may also be good but I’ve never heard it, and both should be a significant step up over the Modi and are within your budget.

https://www.amazon.com/Musician-Draco-Entry-Level-Decoder-DSD1024/dp/B096S6HBQY/ref=sr_1_1?crid=2OF0N1L15MRC5&dib=eyJ2IjoiMSJ9.zW5BR7hQ685y2z_-Sro1MNRZ1c5rUbXxAV-S4ldTGy7iEjFYc_JgVbrDqWN2tLkAT5_8XmSfqQV0PiJ064tlyFbqiFedgTKMRAeIvQxhFDxxAsTA_M36Si21yQ-ww-8QV1vLs5N_PNGeMGyZZZFAHgW2jkipOwQKomMqgoPbZjclblj-OfY5qMyNStTjLKBP4blHhYhiFMT834XVkvXiOnW46iEwilckAOsar9ZuJN6RmvpIFiXwIGeS5GBBMcUhAknnZFzMHo8bCyC8DOZmHsM4I05usPL0WaYayvCivmQ.155I36q9t-GX2F5drwS3LGOOw1RWpFqlethxAZZyr-Y&dib_tag=se&keywords=Musician+Draco&qid=1724096731&sprefix=musician+draco%2Caps%2C85&sr=8-1&ufe=app_do%3Aamzn1.fos.2b70bf2b-6730-4ccf-ab97-eb60747b8daf

For cables I’d recommend LavriCables that offer very high performance/$.  Here are the balanced cables I use to connect my DAC/Amp and the headphone cable.  Several others here have used their cables and have been universally very happy with them and found them to offer a meaningful improvement over what they were using before.

https://www.lavricables.com/cables/reference-silver-xlr-interconnects/

https://www.lavricables.com/cables/ultimate-silver-headphone-upgrade-cable/

Last, you’ll want a good digital cable to go from the Node to the DAC (get 1m or 1.5m length), and I’d recommend this DH Labs cable as it offers good performance and value (they offer a 10% discount if you give them your email address)…

https://silversonic.com/products/digital-cables/d-750/

Hope this helps and gives you some ideas, and best of luck. 

Thank you for the detailed response. If I cut my budget in half to $1000, what would you recommend?

I’d still get the Singxer amp and probably the Schiit Modius DAC. For cheaper interconnects and digital cable I’d recommend these from Pine Tree Audio…

https://sites.google.com/view/pine-tree-audio/interconnects/balanced/iso-braid-balanced-cables

https://sites.google.com/view/pine-tree-audio/interconnects/single-ended/nexus

I’m not well versed in cheaper headphone cables, but this would seem to work for your headphones…

https://www.amazon.com/Youkamoo-Replacement-Upgrade-Compatible-Headphones/dp/B08LF2N88J/ref=sr_1_5?crid=24YZRFAKRUZHP&dib=eyJ2IjoiMSJ9._nS8NgqIUalZvgaeqfvc23zpFp4bRZVCoe2ED9oUEm3TYy9IJ1h7tATN86agc4q8_I6WrzPxwGDS5MEFLJjn_cyI8FExWXttxJkW2Q9dpJG-IuPG7tz2LmhLtHmbmZyj2rj0nQzieO421e8Mg_xE9kIfKkPMj4poCs7DNdTCXuumr-Th44Kb_euin72aqLVni_uZ3iEemIFaiCoOsaUCN6Jle0MCZppye82szFeiRVLq3QvMeFNST7j31QwHVYJyfIw0sDgxBzkJOvmkvSHNUb23_vShkzaJbbSGuwKyp-U.6bkcO_Cd-IWQ5yds8TVCv2w_P3xDTQ6-Ti1Hz-koODY&dib_tag=se&keywords=balanced%2Bxlr%2Bheadphone%2Bcable%2Bsennheiser&qid=1724122870&sprefix=balanced%2Bxlrheadphone%2Bcable%2BSennheiser%2Caps%2C578&sr=8-5&th=1

Look at Schiit Jotunheim with a built in DAC.

Look at Schiit Jotunheim with a built in DAC.