First gaming PC advice needed.

Figure out your total budget for cpu and graphics card.
Allocate 1/3 to the cpu and 2/3 to the graphics card for a balanced gamer.
With your budget, using an intel cpu is probably best.
Probably a i3 or i5.

It depends if you're trying to go purely gaming or not. Will you be ocing? Any Video editing? If it's just for games i believe you can find a cheap cpu i5 4430 about 180 thats without overclocking and thats the cheapest price per performance you're gonna find. You may want to buy a non/factory air cooler i'd recommend a hyper 212 plus usually for about 20-30 bucks on amazon, you don't actually need it, the stock fan should be fine but it's a nice thing to have i suppose plus if you live in a really hot area better safe then sorry. The case another important part of your build. I'd recommend something from corsair maybe a coolermaster hafx, but thats a full atx case i'd probably go mid atx save money and it'll have decent airflow you could probably find one under 100 look on tom's hardware forums you'll find some pretty good ones. Ram i'd get 8gb a lot of games require 4gb minimum or more now a days http://www.newegg.com/Product/Product.aspx?Item=N82E16820231667 its about 80 bucks decent ram, brand doesn't matter if you're not ocing so you won't have to worry about cl and how much mhz the stick has etc. and so forth. The motherboard http://www.newegg.com/Product/Product.aspx?Item=N82E16813130779 this msi one should do or any z87 moba really. For around a 100 usd. Finally the psu this depends on your gpu i'd say 500 watts should cover most everything http://www.newegg.com/Product/Product.aspx?Item=N82E16817153166&nm_mc=KNC-GoogleAdwords-PC&cm_mmc=KNC-GoogleAdwords-PC-_-pla-_-Power+Supplies-_-N82E16817153166&gclid=CjwKEAjw8O2hBRDKur2lseLW6C8SJAC-r1J3xldi19Z7GdXBZ6y0pT7ML_2fv7epdOw4_NV8N5laPxoC9hbw_wcB.

Also forgot about the hard drive which depends on you but for $100 you can find a 1tb hard drive if you spend an extra 20 you can get a hybrid, but i'd go for the 1tb without the hybrid ssd.
I hope you have an O.S. already.
Alright quick math 500 euros = 780 usd
500 watt psu $50
cpu i5 4430 $180
Case mid atx $100
Ram 8gb G.SKill $80
Motherboard MSI $104
HardDrive $100
Total = $614 with lets say 40 dollars of tax guestimate could be more could be less
leaves you with 126 usd to spend on a gpu and i'd get at least 1 to 2 hundred if you want a decent rig that'll last you a good while. GPU's are an integral part of your pc. Also i'm assuming you have some sort of monitor already because that alone would make you go way over budget. A really good GPU depending on your personal preference would cost at least upwards of 250 to about 300 like the gtx 970 or the ati r9 equivelant. Though with your budget i'd shoot for a gtx 770 or 7970 look for some used cards you might get lucky or you could go to the mid range cards like the gtx 600 series or 7950 and lower. Which all depends on the kind of gaming you'll be doing if its 4k then you're going to be waaaay over budget.

It depends if you're trying to go purely gaming or not. Will you be ocing? Any Video editing? If it's just for games i believe you can find a cheap cpu i5 4430 about 180 thats without overclocking and thats the cheapest price per performance you're gonna find. You may want to buy a non/factory air cooler i'd recommend a hyper 212 plus usually for about 20-30 bucks on amazon, you don't actually need it, the stock fan should be fine but it's a nice thing to have i suppose plus if you live in a really hot area better safe then sorry. The case another important part of your build. I'd recommend something from corsair maybe a coolermaster hafx, but thats a full atx case i'd probably go mid atx save money and it'll have decent airflow you could probably find one under 100 look on tom's hardware forums you'll find some pretty good ones. Ram i'd get 8gb a lot of games require 4gb minimum or more now a days http://www.newegg.com/Product/Product.aspx?Item=N82E168... its about 80 bucks decent ram, brand doesn't matter if you're not ocing so you won't have to worry about cl and how much mhz the stick has etc. and so forth. The motherboard http://www.newegg.com/Product/Product.aspx?Item=N82E168... this msi one should do or any z87 moba really. For around a 100 usd. Finally the psu this depends on your gpu i'd say 500 watts should cover most everything http://www.newegg.com/Product/Product.aspx?Item=N82E168....

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OP is in the EU, links to Newegg won't be of much use.

What is your country of origiin and what store are you buying from? Knowing those things will help to suggest a system. If you don't know of one this thread will point you in the right direction: http://www.tomshardware.com/forum/id-1643019/guide-international-users-links-part-stores.html

I thought AMD was always better for budget builds.

I'd personally go with a Pentium G3258 depending on the budget.