One of the key differences in film vs. digital photography is in the output. For most people, film is easy -- you take your roll of exposed film somewhere, get them developed, printed and returned to you in a nice brightly colored envelope. The most important thing to keep in mind here is you print them ALL out. With digital its typically very different. As mentioned in numerous articles, there are typically many many more pictures taken. One way for you as a user to get your photos printed is to purchase a photo printer for your home computer system.
Once you've decided on the right printer for you, now you've got a very big set of decisions to make and that's 'which is the best paper for me to use'. If you're a typical person that's interested in taking snapshots of people and filing them away in an album or handing a few out then the decisions are actually fairly easy. The first part of the decision is which brand of paper to use -- that's easy, use the brand distributed by your printer manufacturer in their name. This is simple because these papers are guaranteed to match your printer settings for that particular type of paper. Most printer manufacturers (Canon, Epson, HP) offer a variety of papers and other surfaces for you to choose from. It wasnt long ago that home inkjet printers would print out your photograph and the image would last for 1 to 5 years before fading out. Today, standard inkjets will produce images that will last for between 5 and 10 years (depending on environmental conditions). Some of the better papers that are available will produce prints that can last from 25 up to 120 years (i don't know what lab has had inkjet printouts for 120 years, but I'm impressed).
If you want to check out the life expectancy of your prints, head over to Wilhelm-Research.
There are a few things to consider when selecting the TYPE of paper that you will print on. The first thing to consider (and for those of you sticking with your manufacturer, the ONLY question) is the Surface. All photo papers are coated both to hold ink and to look like photos. The coating varies from Glossy (shiny) to Matte (non-reflective). Choosing between these two is both a matter of taste and what you want. Glossy paper will make your prints look like what you get from your color lab, but are easily smudged. Prints on matte paper have gentler color tones that are easier on the eyes. Matte is great for black and white or for pastels, the paper wears better if handled frequently. For those of you that want something in between there are other paper finishes -- satin, semi-glass, velvet and pearl.
There are few other features to consider with paper. First is its Opacity. The opacity of most photo papers is typically high (in the mid 90s) -- the higher the less likely that ink will bleed through the paper. Opaque paper is great for double sided printing or for business printing.
Another consideration boils down to taste. That is in the whiteness of the paper. In most cases, whiter is better, but there are a few applications (watercolors as an example) where white paper is less desirable.
Some additional paper resources (non printer manufacturer resources):