Exclude Categories

So, it’s an age old problem, based on what I’ve seen online.

Basically. I have 3 pages which use 3 different templates (so I have the ability to add script to the page or the .php file)

On each page I want to display a list of archives from a specified category.

Example:
Insperation Page: Displays a list of posts posted in the Insperation category
Captions Page: Displays a list of posts posted in the Captions category
Updates Page: Displays a list of posts posted in the Updates category

Any ideas? I’ve tried include and exclude plugins, variations in the scripts and variations in the page but nothing worked so far.

I’m confused as to why this appears to be such a difficult task but any help is much appreciated.

~ Tirwin