I like to comparison shop and have no problem doing the homework.
You will be well aware then that in order to get the spec of computer that you need will cost you circa $400 minimum.
Purchasing a Windows 8/8.1 platform computer now will ensure that you do not have to pay for it when Windows 7 is retired in a couple of years, turn the new metro and other Windows features off in Windows 8/8.1 and it is just like Windows 7 but faster.
Intel CPUs are commonly more expensive than AMD CPUs.
For your intended use an AMD or Intel i3 CPU is adequate + it will help to keep you nearer to your budget.
The average user will not utilise all 4 cores of a quad core processor even when gaming, this will change in the coming years as software becomes more demanding.
AMD APU CPUs provide integrated graphics.
CPUs that have unlocked cores so that they can be overclocked are more expensive than the locked version of the core, an example of this is the i5 4570k unlocked CPU costs on average $10 more than the locked i5 4570 version.
You should select a computer that has 4 cores or you may find yourself needing to upgrade again in 2-3 years.
CPU benchmarks here
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