Why can't I install php-mysql?

The package is called php5-mysql in Ubuntu, not php-mysql.

Easiest way to install LAMP on Ubuntu is using an APT task:

sudo apt-get install lamp-server^

^{The caret (^) is not a typo.}

It will select all the relevant packages for you. For your specific case is Dennis right, you're just missing the PHP5-MySQL bindings which you were installing with the wrong package name. Anyway, the task will make sure you'll have most common packages, including this one.