You need to fix somethings.. Windows ...... what home premium? Vista and Win 7 both have that. 2MB should be 2GB. It does not really matter much to your question, but you should at least know how to explain what you have.
You won't be playing a lot of high-end games at right res on that system with any video card, but a Radeon 5570 should run in just about any system and will be a huge upgrade over the 1300. Just make sure you don't have a 200watt power supply or something and that the case will fit the card.