With digital colour pictures, it would probably good idea to use glossy paper to give your pictures a glossy look, much like photos that are taken with a normal camera. When printing out on glossy paper, you need to select the 'glossy' option in the print menu.
If you are putting your pictures in a frame, then perhaps printing out the pictures in 'best' quality on normal paper would be okay, as the glass of the frame will provide the glossiness.
When printing out digital pictures, it is a good idea to print the image in 300 dpi (dots per inch). You can change the dpi in a photo minipulation such as PhotoShop and you may need to alter the size of the image in addition to this, such as making the image smaller.
Before printing out ay images on glossy paper, always do a test print on normal paper first to check that image prints correctly (this saves you wasting expensive paper).
I would also say glossy, but then, when you print it at home, make sure it is not the first and cheapest paper you can find.
It also depends on how much you will be handling the photos. Glossy gets fingerprints easily, so if you go glossy, put it in a photo album as soon as possible.
Matt paper however doesn't show fingerprints, but the clarity is sometimes lost on matt because of the textured paper.
That also depends on the dpi of the image you are printing. If it is 300 dpi, it will be perfect. If it is 72 dpi it will be of poorer quality.
The best paper to use would be special picture paper that is shiny.
The kodak satin finish does the best to me.
I get the best results when I buy the same brand of paper as the printer I am using. After that, shiny or semi-matte works.