As always, you get what you pay for.
Audacity is pretty good for a free DAW. But it's not great; it is woefully lacking in features, especially those needed for audio post.
I know lots of folks like Reaper; however, quite a few I've talked with have mentioned video playback issues (among other audio post related problems).
The M-Audio line of Pro Tools starts at around $250; you get Pro Tools Express software and a very basic USB audio interface. Pro Tools will also work with other audio interfaces, but not quite as seamlessly as with Avid products, especially on PC platforms.
Digital Performer and Nuendo are the other major competitors. There are other DAWS that do an okay job on audio post such as Cubase, Ableton Live, Sonar and a few others, although they are more music oriented and could possibly have video playback issues.
The one big reason to go with PT is you are compatible with 99% of the audio post houses out there. Another is that, even if you are using PT Express, almost everything you learn will be applicable to full blown HD systems - the basic structure is the same, so you're not learning a new software.
Besides the software (Softwear? Is that something like a digital sweater?) you need some decent speakers and a relatively quiet, treated environment. One mic of good quality is very helpful as well.
As always talent, knowledge, skill and experience go a long way.
I'm sure you know the old joke about owning a boat; it's a hole in the water into which one pours money. Well, audio post is sort of the same way when you're getting started - it's a hole in your basement (bedroom, living room, whatever) into which you pour money. But if you seriously want to pursue sound-for-picture, more specifically audio post, there are some things that you absolutely must have.