We want to track users to our website but manage the data collection ourselves, we do not want to record bots but real visitors. Should we use jquery or some other kind of plugin?
To create your own data collection scripts would require lots of things: Javascript and/or jQuery, PHP, a database, and quite a bit of time. You could use JavaScript or PHP to get information about the visitor on each page they visit.
Unless you are ready for a pretty heavy time investment, I'd suggest going with an open source alternative platform. I suspect this is what you're after, but I might be wrong.
The following have extensive dashboards that provide pretty good information. They are both PHP programs that live on your server and save information in a database on your server. While not as simple as using Google Analytics or similar, you have control over the data and a lot more functionality.
Open Web Analytics:
http://www.openwebanalytics.com/
Demos: http://demo.openwebanalytics.com/
See install instructions here: http://wiki.openwebanalytics.com/index.php?title=Installation.
Piwik:
Demo: http://demo.piwik.org/
Install and configure: http://piwik.org/user-guide/ Install video: http://piwik.org/blog/2012/10/how-to-install-piwik-analytics-video/
Update: Piwik is now called Matomo - https://matomo.org/