Dot-matrix printers were cheap, not much more than a decent ink jet today, but the quality was abysmal. Starting around 1991, ink jet printers changed all that. Arriving at about the same time as Windows 3.1, they helped ensure its success. And the quality was almost as good as a laser's, which has always been a little more expensive because it has to work with a full page of data at a time. About the only reason you'd use a dot matrix printer today is to fill in pre-printed multilayer carbon forms.
More expensive models are also capable of higher print rates and higher resolutions than ink jets.
With those exceptions, ink jets are where the action is today for home users. If you try to print text and graphics together, blacks are produced by combining colors, which usually results in an ugly greenish tinge to your type. Better printers allow you to use black and color cartridges simultaneously. You be the judge, and keep in mind that less resolution generally equals faster print speeds and less use of consumables. On the other hand, if you're printing photos, the extra dots allow for more, and far more accurate, shades of gray.