Proper way of removing/hiding unwanted elements?
It depends what you are hiding.

If it is something like a page or block title or labels or other semantic type markup, you should hide it using the element-invisible class, which effectively hides it but without using display: none. This way screen readers can still see the text, which helps give visually impaired users context for the subsequent content, which is required for accessibility reasons.

If you are hiding actual content, like fields, or whole blocks, or menus etc. you should not be doing it in the CSS. It is best to do it on the back end.

The time when this is most important is hiding for access control. Never use css to hide data or fields that a users should not be allowed to see. Because that data is still available to the user, it just isn't visible by default. So that would be a security issue.

For forms you can use hook_form_alter(), hook_form_BASE_FORM_ID_alter() or hook_form_FORM_ID_alter().

For other areas, there are many possibilities depending on what you are themeing and what you are intending to do. Some examples, are hook_node_view_alter() for node pages, hook_user_view_alter() for user pages, other alter hooks, template preprocessors, theme functions and template file overrides.

For more information on drupal hooks see http://api.drupal.org
For more information on overriding theme functions and template files see http://drupal.org/theme-guide/6-7