In theory, you already have all you need.
The upside of a USB mic is that it does the conversion from analog to digital for you, so no separate mic preamp is needed.
Once in the digital domain, then to all intents & purposes one DAW is as good as any other.
What you would gain from a 'better' DAW is in the editing, mixer bay & audio plugin areas - though Audacity has equivalents for a lot of those.
A better DAW starts to become a necessity once you exhaust the possibilities of your existing setup.
There's a lot of mileage in your freeware setup; work with it, experiment with plugins - compressors, reverbs, EQ - etc. - until you are sure you have extracted the most from it that's possible... then look at the paid options.
If, as it sounds, you are doing what is effectively 'adding a vocal track to karaoke' then you may never actually need to step up to a paid solution.