The most comon color printers are ink-jet printers. The best way to pick out a color printer is to go to a store with several different models and brands to choose from, look at the sample print-outs and ask questions.
Additional colors can also drive the price of the printer up.
The printer may have 1 cartridge with all 4 colors of ink or seperate cartridges for black and color or even seperate cartridges for each color. The advantage to more cartridges is you only have to replace the cartridge that is out of ink. For example if you run out of a single ink color lets say cyan. On a printer with just one ink cartridge that has all 4 colors you have to replace the cartridge and wast any remaining ink of the other colors. A printer with seperate cartridges for black and color, you would only have to replace the color cartridge, this would still wast the rest of the magenta and yellow ink but the black is saved.