are pretty useless to be honest. They count total page requests, rather than unique visitors, and the sight of one on a homepage just screams 'amateur site'.
Server stats are very useful, and analysis depends on what information you need. To most people the important statistic is the unique visitors total; this tells you how many individuals visited your site. You'll also have information about the page requests, page by page, and this can be very helpful if you're running a commercial site - it tells you what your visitors found most interesting.
I have never used any form of analysis software, because I don't think it necessary - an Excel spreadheet can tell me everything I want to know, especially if I use the graphing facility.