Looking for REALLY low budget entry gaming PC

Hello,
I would like some help and reccomendations on buying a really low budget gaming PC. I'm from a different country, so prices may vary, but I will convert my prices to us$.

My budget is around $250, and I don't need a monitor or OS. Mainly, I want to play League of Legends with good fps, on high graphics if possible, and some other old games (the newer the games I can play, the better). For non-online games I consider 20-30 fps good enough.

Given my tight budget I was planning on building around an AMD Trinity APU, more specifically, the following (I'll also include the best prices I can get in my region):

CPU: A8-5600K ($88)
Motherboard: Asrock FM2A55MDGS R2.0 ($52)
RAM: 2GB DDR3 1333 ($22), and planning to add another 2gb later.
HDD: 500GB WD Caviar Blue
All of this inside a $38 case with generic PSU and keyboard/mouse/speakers included in price.

As a second option, I have a 120GB semi-old HDD laying around (I'm 「almost」 sure it works), so I could save $50 off that, and use that money to get the following:
Option 2: AMD FX-4300K with motherboard ($140) and Radeon HD6570 ($60), no HDD. The rest is the same
Total: $260

Option 3: i3 3220 with motherboard ($140) or maybe i3 3240 with motherboard ($150-160) and Radeon HD6570 ($60)
Total: $260~$280 (that's a bit too high for me)

I can't really go any higher, but I could improve some minor parts in a few months (RAM mainly, and HDD in the 2nd/3rd option). Maybe also change the stock cooler for a $30~$40 cooler later, for some basic overclock.

Is there anything you would reccommend changing? In case you suggest any parts I'll post the best price I can get for them here, if available (for example, reccommended Athlon X4 750K is not available here).


Just to be more specific for whoever is interested: I'm from Argentina and I get the best prices at http://www.mercadolibre.com.ar/ , so if you know spanish you can check yourselves. Exchange rate here is us$1=ar$10 (don't trust official/websites exchange rate), and my budget is around ar$2500.

Thank you in advance for your help,

Anbell
 
Hey, I'm i late for the reply? 😛
So mate if you want that low budget PC we can chop a bit off the price if you re-used some of your old systems parts (Hard Drives, Opticals Drives etc.)
What are your Specs?