I've found a shareware log analisys tool, I'm just beginning to test it, but I found it great so far.

Its name is Summary; the homepage is http://www.summary.net. You might want to check it out.

For a similar price, I think sawmill is a much better tool. It has filters and really allows you to drill down with more detail than summary. http://www.sawmill.net

I'm pretty new to this whole web hosting business. How do these applications compare to free tools like Webalizer?

Sawmill is much better.

Posted by Duncan
I'm pretty new to this whole web hosting business. How do these applications compare to free tools like Webalizer?They provide different level of details. Webalizer is likely to produce very shallow stats. More powerful analyzers let you dig much deeper. They can help you to see typical surfing routes, top entry/exit pages, most/least popular pages and so on.
Still it’s to you to interpret these details right. The hard part is to use the data to improve your business.