You will notice that a few degrees can make a world of difference so trial and error will show you the best final rotation amount. After finding the optimum setting for your rotated image you will notice that it has become a little fuzzy, this is typical and can be corrected with a sharpness effect. Most all paint programs have a sharpness filter or effect, use it to clarify edges and brighten the scaled image back to its original condition. Again, trial and error is the best way to apply sharpness, start with a little and gradually increase it until you are satisfied. Now you are ready to save the finished image back to a .gif file.
Some paint programs convert the image automatically as discussed in the optimizing tutorial.
Others may require you to manually convert it back to 72 DPI and 256 color before your save. Never perfect but sometimes adequate. You won't achieve the results of working with a high res image as the source file but sometimes you can get close using the procedure above.