Photo paper gives a truer dimensional photo - there are settings for printers to tell it which kind of paper you are using, make sure to select the correct one. When using photo paper (glossy or matte) the image is usually richer in colors.
Which program do you use? Paint Shop Pro has several ways of resizing images - some are just a pixel resize (which leave jagged edges) - I use a "smart size" but there are also "bicubic, bilinear, and weighted average" options. Check your program for sizing options -- I often create for 8x8, yet print most at 6x6 and have no problems. Shrinking causes fewer problems than stretching.