Personally, I think sound is more important than picture quality. (I can’t understand why people always think the other way around.) And there I got a question. Which is better for sound editing audacity or HitFilm Express?
You can get a free version of Pro Tools called Pro Tools First. But if you're using Premiere presumably you've also got Audition? That comes with some good noise reduction.
I own the Pro 8 version of HitFilm and I would use dedicated multi-track audio editing program, such as a Digital Audio Workstation (DAW), with VST plugin support for audio editing and mastering.
As a long time musician, I personally have several DAWs in my music studio and have never used Audacity. However, to my knowledge, Audacity does support VSTs, which will open up more available tools to edit the audio tracks.