Will this graphics card be sufficient for a gaming computer?

I have heard that with gaming, the graphics card is the most important part of the build. The one that I got suggested to me is Asus AMD Radeon HD 7850 DirectCU II Graphics Card (2GB GDDR5, PCI Express 3.0) . Is this card good enough for games like Battlefield, Minecraft etc. On high settings? If not, it would be greatly appreciated if you could suggest one.
My second is that I have been getting my parts off of Amazon. Is there another trustworthy UK website, that I could buy the parts from cheaper?

It would certainly be fast enough for those games. It's only been out a year or two now. The second digit (in 7850, the "8") is the number that hints at the card's performance.

In AMD's numbering scheme, the second digit denotes what the card is designed for. 2-4 is low-end, 5-7 is mid-range, and 8-9 is high-end. This is an "8" card.