Vett... this is from the heart!!!
Look at my System Specs... nobody is on a tighter budget than me. I am a habitual penny pincher
Now, being said that, if you want to play Crysis 3 so bad, you are going at it all and completely wrong... and I mean with the out most respect and only looking to help.
C3 is extremely heavy on a computer, perhaps not as hard as C1 was but stll tough and if you want to skimp on hardware, you will only be wasting your money... anything less than a GTX660 2GBs (or a GTX550Ti) will put a heavy burden on your system and you'll be lucky to play at minimal settings with 15 frames per second.
Can I prove it? Not 100% but again, being on a tight budget I did my research and my homework and I waited about a month and a half to be able to get what I needed. All I can tell you is... be patient if money is tight right now... save a little and be happier later playing C3 and then the other newer games coming down the pike.
Remember, I was told that anything less than a GTX was not going to do the job and a GTS is lower. If you are still dead set on it, I do hope that I am wrong.