If you want to change the look and feel of a PAGE to wordpress, you will want to look at page.php. This is the template file for the theme you have selected, located in the themes directory /wp-content/themes/UR_THEME/page.php
If you want to change the look and feel of a BLOG POST, index.php is your man.
In WordPress, a PAGE does not have categories but can have comments.
A POST can have categories and tags and comments.
Typically you would use a POST to create a new blog item and a PAGE to create a static web page like About or Contact ME.