I still don't get the need for a USB mixer. Explanation, please - home karaoke = singing along with prerecorded tracks. Are you trying to record the singing to tracks on a computer and the backing tracks are on the computer? If so, then an interface would be the best solution, you add reverb, EQ in your DAW.
If you are not recording, just singing, use a karoake machine!
This one will even record onto an SD card.