My suggestion would be to get a bigger PSU which would cost around $50 or $60 and go with a more powerful card. For what those 9600GTs cost its not worth it IMO. But If you were to get the 9600GT it should't have a problem running on that system.
What games do you intend to be playing with this? Also are you serious about gaming or do you just want to play here and there?
I am going to seldom run games, but I would like to be able to whenever I want. I am concerned about the 9600 GT because the specs indicate a minimum of 300 watts in the power supply. I worry about the heat and the lack of power over the long term.
I have this computer and upgraded to the ATI / Saphire 5570 from Newegg. It unlocks DTS-HD and True-HD Audio and the actual HD video is noticably improved over the stock card. After adding the card video conversion time is reduced by about 60%. The card is supposed to be ok/good for gaming (but I dont use my PC for that).
I have no issues with it overheating and the card with its fan fits into the slot with no problem. It took about 5 minutes to install it. Research this card. Others bought with the same system it before me and reported good results so i took the plunge and am happy i did.