Hi Gort,
We here at ShapeTapes recommend Reaper -
http://www.cockos.com/reaper/ - The evaluation version is complete and "uncrippled", and it's free to download (the discounted price for most buyers after the eval period is only $60, and it's well worth it!). Reaper is fairly simple to get started with. As with most programs, there may be a few stumbles along the way if you're using it for the first time, but overall we find the program to be very user friendly, stable, and versatile. You'll want to explore adding plugins, but that's a different topic. Another software you might want to check out is Audacity -
http://audacity.sourceforge.net/download/ - it's a free audio editor for PC, Linux or Mac OS X.
Look for more about DAWs in digital recording section of this forum later this month.
Welcome to the forum!