<< an image is likely to look at its best printed out if you have about 300 pixels per inch >>
That is true. Did you also know that if you print at larger than 300ppi your printer may endup creating artifacts in the photo?
300ppi is not the most pleasing resolution. Rather, it is the maximum that most printers offer theses days.
But I agree, you do not need to print at 300 ppi to have a good print. A 150 ppi with a good tonal range, white balance, and such looks just great to the average veiwer.