Im thinking of buying some new components to my computer. Im interested in buying a new graphics card, processor and because of those i have to buy a new power supply. The budget is ~300? maybe a little more.
That setup upgrade looks fine, although I am not real sure that Chieftec PSUs are reliable. Also, since you're running a 8800GT I would go with a 500watt.
Not to mention that you need to include another gig of ram. 1GB is bare minimum these days, maybe not for CS, but for COD4 and Crysis, 1GB is very little.
Chieftec PSUs are terrible, you will need to spend a reasonable amount of money on a PSU, it's not just a case of "it's cheap, it'll do" most cheap power supplies will very easily fry all your components and are also well known for fires. That PC will run fine off a 400W power supply, but you need a decent one.
Try and find a Corsair VX 450W.