In the market for a CMS

Hello all. I've come in charge of a small but long-running server which serves principally as a signup site to use on-site equipment. There's only about 12 machines, though there are numerous users (the majority of which are inactive by now). Unfortunately the DB structure is so terribly sloppy that I convinced my boss to let me overhaul the entire thing, but I'd much rather not do it by hand.

The front-end is simple enough. Users log in, select which machine they wish to use (assuming they have permission to use it) and then select the date/time. THAT'S IT!

On the back-end, of course, I'm looking for scalability (though I doubt we'll go over 15 machines... ever), and more importantly reporting capabilities. A billing system could be a good thing. Definitely looking for a LAMP system.

Also looking for ease of use, as I will hand it over in less than 9 months. On that note, I can't get TYPO3 introduction to run on my local PC  :'( (I suspect it's because I already have the current website running locally as localhost)

Your recommendations are appreciated.

CMS's are designed for people who have a publishing application. There is nothing a cms is going to offer you that is useful given your description and requirements.  If I understand you, this is a scheduling application? 

The 2 most used LAMP cms systems are Joomla and Drupal. They both have the ability to have user login systems and have commerce and subscription management modules available.  For the scheduling of the machine pool, you're going to need something custom with either one.  In other words, you'll need code, and understanding how to develope your own module in either cms is non-trivial even for experienced php developers.