PHP is your best bet, if you're still on dayjo's server then it's already installed, and it's very simple and easy to learn.
If all you want is to log votes and IPs, you could do a simple thing storing them in a text file, or you could use MySQL, which is what, for instance, SMF uses.
While you're at it, you could write yourself a nifty little uploader script which would update the site automatically. They're not too hard to make, and if you're updating all the time it's very handy to be able to just use a web based form, rather than FTP.
Anway, the place to start is
www.php.net . There's tutorials and the entire function reference there.