These sorts of advanced functionalities usually aren't included in any CMS. You usually get 3rd party plugins and *extend* your default CMS installation with the addons and plugins that you need. Joomla is quite nice and extensible, and there certainly are a lot of different plugins for it. But you don't need to install them on a Live website to test them. You can just install WAMP server on your computer and install Joomla and play around with the plugins. If you don't like it, uninstall it and try another one. Or try out the demos, or read the instructions, however way you go about it, the end result is: Find the right plugin that does what you need it to do. Also there's lots of places where you can scan the code for any hidden nasties with base64 encodes.
And I don't know much about Google Analytics as it's not really my specialty, and I don't know if it can track Banner clicks, but Google Analytics as far as I'm concerned tracks *most things*, including the areas of your pages that have been clicked, where the users leave their cursors, how many visitors you get and where they from and what browser/OS they use, how they got to your site either via search engine or direct access etc. You can make reports based on a time/date selection to present to your clients/bosses, identify areas of improvement/optimisation etc...
I would probably go for Google Analytics in any case, and if you found a nice Joomla component which tracks/collects user statistics too then it certainly *will help* rather than do harm i reckon.
Hope this is useful.