Resolution
First and foremost, the most important criteria when choosing a printer is the resolution measured in dpi (or dot per inch). The dpi will determine the quality of the prints. Choose a printer that can produce photo quality prints. Typical photo printers has a resolution of about 2400 x 1200 and if your looking for the best resolution there are printers out there that can have a maximum resolution of 4800 x 1200 dpi. If possible compare the print output of the printer and those printed from a photo lab.
Inks
Ordinarily printers, typically has 3 ink cartridges, but if you want your photos to really come out with those near photo quality, you can choose photo printers that have more that 3 ink cartridges, When choosing a photo printer, the more ink cartridge the better. You may also take into account the ease of replacing the inks, the price and the availability. One other thing to consider is, if the printer you are buying can take 3rd party ink especially if you are price conscious. When all know that original printer inks are very expensive.
Photo Paper
Photo printer manufacturers usually produced their own photo papers. But there are also third party manufacturers of photo papers. You should take into account the availability of third party photo papers. This may save money for you in the long run.