As Armistice says, your software isn't the main contributor to your sound quality. Your hardware and your skills make the most difference.
In general the most important hardware is, in descending order of importance, the microphone, the preamp and the converter. Your skill and experience affect how you select and place microphones, how you set your hardware and how you mix, all of which have a huge impact on the sound.
Software is more about features and workflow, in which terms Audacity comes up short for multitrack recording. Reaper is your cheapest good option, and it rivals just about anything out there.