It sounds like the simplest and most flexible approach is to find a plugin that creates a widget for you that you can configure to display any post of your choosing in whatever fashion you prefer. Then you put that widget in the sidebar that appears on all of your pages. I would not develop this custom because it is an obvious problem that others have solved many times over.
In other words, there are plugins out there that do just this. For example, I found a couple of plugins in a Google search: Ultimate Posts Widget and Flexible Posts Widget. Many robust theme frameworks also include this feature, such as Themify, just to name one.
A second approach in the same vein is to install the Display Posts Shortcode plugin, and then put one of their configurable shortcodes into a Text widget that resides in your sidebar.
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