Image hints
Image brightness
Before beginning processing, it is recommended that you check whether the image you are processing is light enough overall. An LCD screen, as virtually all Macs have these days, can present images with a darkish overall balance with a pleasing contrast and subtlety. Furthermore, the angle at which the screen is presented to you can make a significant difference to how light the image appears, and it can actually be somewhat darker than it might appear. If you are unsure, it's recommended that you perhaps tweak the image's brightness using an image processing app.
Preview can do this for you:
Tools | Adjust Color | Exposure
(or raise the Shadows value to enlighten the darker shades in your image, or even both).
Alternatively, Photos can also do this:
Edit | Adjust | Light | Auto
will probably adjust it well, with minimal effort.
If you have access to Photoshop:
Image | Adjustments | Brightness/Contrast
Adjusting Brightness up a little, and perhaps Contrast down a little, can even out some of the darker shades.
Either of these will result in a better balanced range of colours for your project.
If you wish to retain the original image in its present state too, don't forget to use the Save As option for the adjusted image - and use this new image for processing by Stitch This!
Colour reduction
If you want to have more control over the colour reduction in your image, and you have access to Photoshop, you may wish to use that instead. It has much more advanced control over colour reduction, using a process known as dithering. 'Dithered' images might appear unattractive on-screen, but not so with needlework projects.
If you do have access to Photoshop, it can create suitably dithered and colour-reduced images, as follows:
Image | Mode | Indexed Color | Local (Adaptive) | Colors: n | Forced: None | Options: Dither: Diffusion | Amount: 100%
(where n is your chosen number of colours).
Bear in mind that it will provide best results if you resize the image to your proposed working dimensions before doing this.
Remember, though, that you still have to match those colours to a thread range, which may well produce further reduction in the colours available for your project.
Saving the resulting image as a .bmp file will ensure that the palette information is stored in the output file.