how many amps does your psu's +12v rail have? if it has enough amps:
under $110, a radeon hd 6670 1 gb gddr5 would be good fit for a 360 w psu. depending on your psu's capacity you might even be able to fit a 5770/6770.
if you can upgrade your psu to a 550 w or higher, 80+ rated one, then 6770 or a 6850. amd's nvidia counterparts at this price range are not as price-performace efficient as amd's. good nvidia cards start from old gtx 460 1gb or newer gtx 560 (non ti). for example:
MSI R6670-MD1GD5 Radeon HD 6670 1GB 128-bit GDDR5 PCI Express 2.1 x16 HDCP Ready Video Card $100http://www.newegg.com/Product/Product.aspx?Item=N82E16814127586
SAPPHIRE 100327L Radeon HD 6750 1GB GDDR5 PCI Express 2.1 x16 HDCP Ready CrossFireX Support Video Card $106http://www.newegg.com/Product/Product.aspx?Item=N82E16814102939
ASUS EAH6770/DI/1GD5 Radeon HD 6770 1GB 128-bit GDDR5 PCI Express 2.1 x16 HDCP Ready Video Card Category special, ends 12/16 $115http://www.newegg.com/Product/Product.aspx?Item=N82E16814121474
SAPPHIRE 100328L Radeon HD 6770 1GB GDDR5 PCI Express 2.1 x16 HDCP Ready CrossFireX Support Video Card $115http://www.newegg.com/Product/Product.aspx?Item=N82E16814102940
look up the review of your chosen card.
edit: tomshardware's 'best graphics cards for money: december'http://www.tomshardware.com/reviews/fastest-graphics-card-radeon-geforce,3085.html