I have Ubuntu which I run as a web server. As you've noticed Ubuntu installs more of a desktop environment by default but it's easy to add the web server packages.
If you are on a dynamic IP address then you could use dynamic dns. As well as the others already mentioned the one I use is http://freedns.afraid.org/
. There is a page that you can download using wget which can be easily added to cron.
The packages I installed (using apt-get install <packagename>) are:
- mysql-server (database)
- Apache 2
- openssh-server (for remote access - sounds like you've already got that installed)
- libapache2-mod-python (optional)
- awstats (for apache server stats)
- phpmyadmin (to adminster mysql db with)
Which gives a good selection of web server related packages.