ClassiPress is a WordPress theme, so in order for you to use it you must first have WordPress installed. You can see the first part of the installation process here on the
ClassiPress installation instructions page.. From there, you can install additional WordPress plugins to the theme if you wish, however you should note that not all of these will necessarily be compatible with ClassiPress. All the functions you actually need for the theme are included in the theme itself anyway, so plugins for the most part are just optional extras.
All of the theme files (.php, .css etc) are included with the download package. So basically, what you see on the
ClassiPress demo, is what you get, with the exception of the categories and ads which have been created for the demo, and the category icons which involved a
separate mod which you can do yourself if you wish.
The psd files are useful for web designers who would use them to redesign the layout of the theme. Many people are happy to use the defauly layout available, so it really depends on how much you wish to change it, and if you know how to use the files, as to whether or not they will be useful to you. In any case, you can always purchase the Small Business Edition licence and upgrade at a later time if you find you do need them after all.