Programs to improve audio quality?
I'm not sure if Audacity has this, but what you need is a compressor (actually an expander, but they're opposite things built into a tool referred to as a compressor). The compressor allows you to limit sound that is above a certain dB level, the expander limits sound under that level, called a gate.  You can set a gate with the compressor at a sound level, cutting out faint background noise but keeping your voice.  This will also cut out breathing noises you make at the beginning and end of syllables particularly Hs and Ss. This technique will not work if your voice is not considerably above the level of the background noise.

Another tool which can help refine your voice, but not entirely solve the noise problem is an eq (equalizer).  Look specifically for a parametric eq; these are the most intuitive. Essentially the equalizer loudens or softens sound based on its frequency.  You can use this to raise the level of your voice, but also soften background noise.  This works particularly well if there's a hissing sound that fills up only a small area on the frequency spectrum.

In terms of the recording environment, ideally you could build a sound proof room, but these are incredibly expensive.  Another slightly cheaper idea is to give your recording room an acoustic treatment, essentially coating the walls in acoustic foam.  This won't solve existing noise problems, but it will limit reverb.  Acoustic treatment is fairly cheap.  Generally you can coat a fairly large room at 50-75% coverage for under $100.

UPDATE: Audacity does have a compressor, but the GUI looks really ugly and unintuitive.  A parametric eq also requires an external plugin.  That said, it's still probably the best free program available.  Something paid and marketed as a DAW (digital audio workstation), would do the job much better.  Something like Adobe Audition, Apple Logic Pro, or Avid Pro Tools.