This is my experience while integrating Joomla with Moodle. Just need to make sure that we are using the right version of Joomla compatible with the right version of Moodle. This type of integration is generally used for online learning courses, systems or for even small universities.
There aren’t many online learning web applications and those which are there, require some heavy fees so Moodle is perfect as it is an open source application and requires no investment in licensing fees like Blackboard and others. It has an ugly user interface so to give a better look and feel, Joomla is a great CMS that can be used in the front end. I do not know of any other cms with which Moodle integrates easily.
Anyway, I used Joomla version 1.5.23 and Moodle 1.6. Please make sure that your web server has XML-RPC installed. Godaddy and 1and1 both created problems for me and you will find that many other hosting providers do not have XML-RPC installed and blame their security concerns for the flaws.
I had my client choose Bluehost. I find it better than most and far better than Godaddy.
So, after appropriate versions of Joomla and Moodle is installed, Joomdle needs to be installed for both the systems. If you search for Joomdle in Google you will find many articles and resources. You can download Joomdle from www.joomdle.com and there is a Joomdle wiki at http://www.joomdle.com/wiki/Main_Page . This is probably your best resource for Joomdle and walks you through all the process of integration. The process is step by step and tedious but in end if everything done correctly it will work perfectly.
So if you have an excellent course that you think you can teach and gather some students by making them pay for the course before they can participate, Moodle and Joomla can be your best and most affordable solution.