My favorite stat package (which I use on my key sites) is IndexTools (
http://www.indextools.com/) but it can be fairly expensive (from $20 to $300 per month for the enterprise version which I use).
For a cheaper solution I use Visitor Stats 2 (
http://www.visitor-stats.com/) which runs on your server (requires PHP and MySQL) and is an $80 one-time purchase. It seems to meet all your needs. It tracks unique visitors by the hour, shows you how many visitors are on your site
right now, and allows you to track current or past visitors' path through your site page-by-page showing their duration on each page (assuming you've placed the tracking code snippet on every page). It has a variety of other good features as well (I particularly like the ability to track pages by custom groups I designate).
It can be installed in less than five minutes and the code, in my experience, is stable and bug free. On the minus side, the developer hasn't released an upgrade in well over a year.
Good luck.