I thought I had given this recommendation before, but it must have disappeared.
I also use Joomla!. In fact, I have just made my first website with it.
It's a commercial site, so I'm even getting paid for it!
Joomla! is nice, although it takes some time to learn for us who have been using the old "from the ground up" methods, but it's a tool for very fast website building and easy maintenance.
Strongly recommended.
But by all means, do what I did: Try several different systems before you decide. The extra time won't be wasted.
I must admit I haven't looked closely into wordpress, but I've downloaded it now and will test it in the near future. It's always nice to have alternatives, but from what I've seen, wordpress makes slow websites that do not conform to modern web standards. At least Joomla! claims to do so, and I won't complain about the speed.
The wysiwyg editor and the HTML editor both leave something to be desired -- and the only way to insert php code into the site is to do it in the template, which is fairly complicated.