Graphic Designers -Which method of scaling images is best?

You can try what we call "The 10% ratio". It's a method commonly used for sizing up low resolution images for comps. You'll open up Photoshop and create an action. In this action you will be resizing the image to 110% and then stopping the action. Then you just hit replay until you have the 200% size. The theory is that because you are only increasing the size by 10% at a time, you're cutting down on the amount photoshop has to interpolate the pixels at any given moment. It wont work to infinity but I think you might be safe up to 200% with a 300dpi image. Think of it this way. If you're stacking books, you'll be able to get more stability if you stack them one at a time rather than 20 at a time. Same thing with upsizing an image a little bit at a time. But eventually no matter how good you stack, the books will get too high to be stable and it all falls down (or your image will get too big and look like crap).