Upgrade on cheap Gaming Computer. Help!

I have a computer that I built with little money and now that I have more money now and I would like to upgrade the graphics card and maybe the power supply. I only have $225 and dont want to spend it all. Please let me know what I can upgrade to play games at a higher fps/quality and just overall computer speed.
My Gaming Computer on PC Part Picker
I was also thinking of getting the Corsair CX430 because the power supply that I have is not even 80 plus and its a really crappy Logisys Corp and im afraid it will frie my whole computer. The Logisys Corp says it is 550W but that is BS because my computer only uses around 200W and it shuts of every time a play a game but the fans keep running. I was think of getting SAPPHIRE 100358L Radeon HD 7770 GHz Edition 1GB but I really dont have any clue. I play games like Farcry 3, GTA IV and maybe GTA V, Leage of Legends, Battlefield 3, and more graphic intensive games.

Grab a 500-550W bronze rated XFX power supply. Should be approximately $60. The OEM of XFX PSUs is Seasonic, arguably the best manufacturer of PSUs.

You can put a middle-tier card in that system without much of a bottleneck. If you don't want to spend all your money, I'd recommend a 7850. It will offer a bigger performance boost than the 7770. Try to grab a 2GB variant of the card. You will play any game on low/medium/high settings at 1080p. The 7850 does come with a games bundle, too. You'll be all set for gaming.