I have the same computer as you. I upgraded to 8gb memory and an hd5770. I can play any game at mostly high settings. You don't need to upgrade your memory, 6gb is plenty. I would suggest a hd5770 or above card, like the 6870. You will need a new power supply without a doubt.
Hello. Yeah, you would need a new psu, 250 just isn't enough for a decent gpu upgrade. What is your budget ?