That card should work out alright in your system and will give you the video muscle you need to enjoy just about any game you could want. Your PSU should technically work. However, I would really reccomend bumping it up at the same time. Pushing that 250 watt PSU could lead to premature failure of any number of pieces of hardware.
My quick reccomendation would be this Corsair CX430 v2
. It's a great brand, nice efficiency, and you can pick it up for $26.98 on Newegg.
I know you probably want to keep the price down as much as possible, but you'll be happier in the long run knowing you have quality power going to all your pc components.