GTX 660 or Radeon 7770?

You will be far happier with a 660 if the price is right with you. However before recommending a card for you since you are new to building PC computers.

1. What is your goal
a. Games you would like to play
b. money you would like to spend
c. Graphic settings you would like to play at.

a=BF3, Minecraft, FPS games.
b=about, 850€
c=at least medium or high

Well, let's think - one is almost twice as expensive, so what do you think?

In all seriousness, the GTX 660 is a near-perfect choice for the money

I think I'll go for the GTX 660, and what is a good i5 CPU for these games?

The 660 is perfect for the range you are talking about performance wise its a far better performer then the 7770. You'll be happy with it.

It truly depends on what your intentions are in terms of the the CPU. IF you would like the ability to overclock the 3570k its pretty much the Top Tier Gaming CPU. However if you aren't after overclocking a 3470 would do you just fine.

http://www.newegg.com/Product/Product.aspx?Item=N82E168...

what model of GTX 660 should I choose then?

It is up to you sir. If you aren't caring about overclocking or a super quiet solution EVGA may be the way to go you can get a signature 2 card. Which supplies a quiet solution just not as quiet as other cards like the ASUS, MSI, or GIGABYTE solutions.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

If you are more into overclocking then I would suggest ASUS, MSI, Gigabyte. All will provide a varied amount of success in overclocking and keep in mind that when you buy a GPU, or CPU you roll the dice on the SILICON lottery which means some chips are able to be pushed higher.

ASUS
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
GIGABYTE
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
MSI
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

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Merry Christmas Mr. Big

Thanks same to you.Merry Christmas!!