300 pixels per inch (ppi) is for High Resolution output. It's what photos in magazines are set at to print clearly off the printing presses. For home use, I find anything around 200 and over to be sufficient to print off a color printer. The more pixels the larger the file size. 72 ppi is strictly for web/screen viewing. Anything made at this size will look pixelated, especially if it is enlarged.
Tips for producing the best possible image
1. Make your image to size. If you are printing on 8.5 x 11 paper set up your file to 8.5 x 11 at 200 ppi (at least).
2. If you are getting images and clip art off the web (google images for example,) you need to find the largest file size (say 400x640pixels or above). If you find an image that's 1"x1" on the web (or 72ppi x 72ppi) and want to enlarge it to 8"x 8" in a 300ppi file, you will be enlarging the image too much and it will become grainy and pixelated. It's best to create or scan your own images as you can then control the input size. You can get around this sometimes by using the artistic filters (watercolor, pastels, paint daubs etc) and layers in photoshop to create an image that looks better.
PM me if you have any other questions.