You're actually going to end up editing up to 6 different image files depending on what you're trying to accomplish.
On your system, go ahead and navigate to C:\Program Files\Stardock Games\Sins of a Solar Empire\Textures (or where you installed the game).
In that folder you will find many TGA and DDS files. You're looking for:
Unit_Hud_Pressed.tga
Unit_Hud_Normal.tga
Unit_Hud_Disabled.tga
Unit_Hud_CursorOver.tga
Unit_Picture.tga
Unit_Main.tga
The first four correspond to the bottom right menu buttons in the user interface of the game when a frigate/capital ship factory is selected. Each image file has a specific label which is pretty self explanatory. 'Pressed' is when the icon is clicked, 'Normal' is the default icon, 'Disabled' is when it cannot be constructed and is therefore grayed out, and 'CursorOver' is when your cursor is over the icon.
Unit_Picture.tga is the main picture that is displayed in the bottom center of the screen when a unit is selected.
Unit_Main.tga is the overlay picture that replaces your ship when zoomed out over a planet.
As far as I know paint doesn't support TGA or DDS files by default. You'll have to use a separate program (Photoshop, Paint Shop Pro...) to edit these files. Make sure you back up the originals, or just create your own mod and use the edited files there.
