Well I've never used Joomla! before but I've developed web sites before. I went to the Joomla! website and started reading about it and from what I can tell it is not something that a complete beginner to Web Development will be able to pick up quickly.
Looking at the technical requirements, your computer basically needs to be a web server in order to run the program. There's not a simple .exe file you click on to start building your website, the program is written in PHP so you need to have PHP installed to run it (if you don't know if you have PHP installed, you probably don't). You'll also need to install MySQL, Apache, and Microsoft IIS.
Joomla looks like a pretty useful program, but if you're completely new to website design and don't have to the time to learn a lot about web development then this program is probably not for you. You will want to find a more simple WYSIWYG web editor that will just output all of the files related to your website directly to your computer. From there you will need to find a host, get a domain name and upload your files.
When it comes to finding a host, if this is a web page that will mainly be viewed by members of your family (averaging 2 or 3 visits a day?) then you may want to look at some free web hosting options on the internet. They typically don't allow for a lot of wiggle room but if this is a small website that won't get much traffic it could be a great (free) solution.
As far as web editors go, the only one I've ever used is Dreamweaver. It has a pretty nice interface with drag-and-drop functionality, although I'm not that familiar with it because I usually just wrote the code by hand. It's not free though (unless you download a trial, which would probably have limited capabilities), but here is one good free web editor I found while searching the internet, it's called KomPozer:
http://www.kompozer.net/download.php
I downloaded and played around with it some and the user interface seems pretty straight-forward. Of course if you don't like it you can look for some other ones, I assume you are familiar with Google
. Or if you want you can still try Joomla!, you can probably figure out how to use it and install everything you need, I'm just trying to suggest some faster and easier options.
Whatever you decide, good luck! By the way, I love the new line art over in the coloring thread!