Yes a video card will help speed up games, although your CPU will hold back anything past low medium ones. 560 would be OK, but check the specs on your power supply. If the 12amp rail and voltage don't add up to about 300 or more I would not put in a gaming video card without a good power supply.
It's worth it, since it will allow you to enjoy many games, except the very CPU demanding ones. One thing though, don't spend extra on a 4gb card, 2gb is enough. Chances are very small you'll find a game that will run good enough at settings which require more than 2gb, but which don't also require a better CPU or a GPU more powerful than a 560.