I’m currently in a similar situation to yours; this is what I’ve found so far:

• Audiophiles recommend either the Schiit Modi or the Topping D10s. I’ve never heard of those brands before but they seem to be trustworthy, given the endorsements they receive.
• There are many USB audio interfaces for musicians. Their main selling point is usually the input channels instead of the headphone output, but if it’s good enough for musicians momitoring themselves while singing or playing an instrument, why wouldn’t it be for me?
• This is one of the cheapest I’ve found: https://www.thomann.de/intl/m_audio_m_track_solo.htm
• I think if a device works with macOS you can assume it will also work with Linux.

By the way:

• USB DAC is indeed the correct term.
• The “white and red plugs” are called RCA connectors.