Keep in mind that the more power you buy, provided it is planned well, the more you computer will live up for newer games. In 2012 I used all the budget I could to get the high-end single chip mainstream consumer GPU (was GTX680 4GB at the time) and the highest i5 (3570k) on a mobo that supports SLI with a fitting PSU. I'm still using this computer and it can play any game I throw at with 45-60FPS, and now I even add another GTX680 for more power to give constant 60FPS on extremely high settings.
Let's forget about the SLI because it's annoying and it requires a higher PSU. Unless you plan to overclock out of the box (which I do not recommend), you could just get an overclockable CPU with its stock cooler to save for now (latest ones are good enough for new CPU's) and then when you need more speed you can get the pro air cooler for it. The stock cooler comes with the CPU so that won't cause more costs. Just make sure the motherboard is a good overclocker and the PSU has enough power for that and the GPU.
I'm saying the above since you're on a budget. Remember, this needs good planning and patience. I had that in mind and got a computer that lived for +5 years and can live 5 more in my calculations while being able to play newer games. Take your time, collect information and come up with your own conclusion.