Hey, there! I've grown tired of playing WoW on fair setting (Only way to get decent fps (60)).
This will be my first pc I'll be building and so I have no idea of which components I should get!
So my budget is 600-800 dollar (Roughly 441-588 euros), Can be any 'trustworthy' website around the world. Thanks!
The guy above has a few good parts. World of Warcraft becomes laggy when you are around players. This is not a graphical problem (your GPU) completely, it's mostly a CPU problem.
It seems like you are relatively new to this entire process so I'll explain something.
There is an age long argument between Intel CPUs and AMD CPUs. Intel is much pricier because they are built with higher quality. I personally go with AMD, and I have saved a ton of money and it runs just as well. When you pick your computer the motherboard must be compatible for Intel CPUs or AMD CPUs.
You can build a very nice WoW computer cheaply when you do an AMD build, I know this because I just did it for specifically WoW too. If anything, try to aim for a higher quality CPU. A nice HD Radeon 7850 runs WoW over 60 FPS maxed at 1920x1080, and its quite cheap.
Like I said, the CPU is easily the most important piece for high frame rates in WoW. If I was home I would link you a build but I'm posting from my phone right now.