~€700 gaming computer

Never built a computer nor have any idea how I would set it up and how to find the right pieces that would even match, or even costs... I know all my hardware parts, what they are for and such, but never really tried making one from scratch.

What are you going to use the PC for? Gaming (AC3, PlanetSide2, etc.)
How much is your budget? 700 Euros, could go up to 800-850 if I find it extreamly necessary
Where are you located? Italy
Are you willing to buy online? Yes, if the shipment doesn't cost and it's quick (I've had bad experiences...)
Are you going to re-use any parts from an earlier build? No
Do you need other peripherals like a monitor, keyboard and mouse, among others? No, maybe keyboard and monitor if it can fit in the budget
Have you already bought any parts? No
Do you have an Operating System (OS)? I can get it outside of the budget

Will you need any aftermarket cooling, such as a CPU\GPU cooler or a watercooling setup? Maybe, my laptops have always overheated, so don't know really

P.S. Ideally I'd want something that could run games like AC3 and Planetside2 on default graphics without overheating and lagging, and if I do it I wouldn't want to buy extra parts for 2-3 years at least without feeling the need to
P.P.S Should I worry about the fact I wouldn't have warranty?
 
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