For all internal competitions, the preferred resolution for Projected Digital Images (PDIs) (to match the native resolution of our projector) is:
1920 x 1080 pixels
This means that you should size your images to fit these dimensions.
To do this, in your editing software, set the width to be 1920 pixels and let the software calculate the height (make sure you have it set to maintain the aspect ratio). If the calculated height is then large than 1080 pixels, set the height to 1080 pixels and left the software calculate the width. Note that for square or portrait images, you will always need to set the height.
If you are using Photoshop, select Image -> Image Size, make sure the dimensions are "pixels" and not "millimetres", and type the required value in the Width or Height box. The other value will change. If it doesn't, make sure you have the "link" button clicked, showing a line between the two values. Finally, click OK to resize. Alternatively, you can use Photoshop's "Export" function to export and resize, which doesn't change your original.
If you are using Lightroom, the easiest way is to use the "Export" function and in the "Image Sizing" section, select "Resize to Fit", choose "Width & Height" from the available options, and enter 1920 in the W value and 1080 in the H value. This will always give you the best fit. Once you have the values set, click the "Add" button under the user presets, give it a name like "HCC Projector" and next time you can just select it from the menu.
All PDIs should be in JPEG format, preferable in sRGB colour space, in order to look correct when projected.