Our youth group uses several avenues for promotion but our biggest is our website. http://www.e5youth.org It wasn't expensive to do, about $50 a year for the hosting account. We used Joomla (an open source content management system) for the site with a $50 template we found at Rocket themes. A youth leader with little web experience keeps the site up to date just by added content like latest news, events etc... using the joomla submission form. All the formatting is automatically handled by joomla making the site look consistent and professional. The youth leader just tells the submission form what the content is and the rest is handled by the content management system.
As easy as it sounds you will need someone who is fairly computer savvy to get it up and running but once it's running it's easy to keep up. You may have a parent or church member in the IT industry who may be able to get it up and running.
Hope this helps!