What do I need in order to upgrade my Graphics card?

Hi there, I've lurked around Tomshardware for a while and found a lot of the threads very helpful, and, since I'm not much of an expert on computers and don't want to risk wasting hundreds of pounds, I thought I'd ask you.

I've been looking to upgrade my Graphics card for a while, my computer is decent I find, but I think it's about time to upgrade,
There are two things I'd like to ask.

1. Will the Radeon HD 7850 fit in my computer/will there be any required upgrades before I can buy this? (I also read something along the lines of a 6 pin connector for the 7870 and I'm not sure if I'll need this?)

2. Is the Radeon HD 7850 a good choice of graphics card to upgrade to? as my budget is around £130 and I found that www.scan.co.uk had the best prices for it, I haven't really looked at Nvidea graphics cards much so I don't know whether there may be a better graphics card for the same price that I could upgrade to?

You can take your time answering this if you want, I'm not in desperate need as I'm not planning on purchasing it right now, (In the next few weeks), I'll post my computer specs below if that'll help, thanks a bunch.

Specs:

Motherboard: Gigabyte M68MT-S2

Processor: AMD FX-4100 Quad core processor (4CPUs) ~ 3.6Ghz

Memory: 8192 MB RAM

Graphics Card: Radeon HD 6570 1 GB

OS: Windows 7

Case: Galaxy 3 Gamers Style Midi Tower Case

So again, I have quite a large computer case, and I know graphics cards come in several different shapes and sizes, but I'm not quite sure how their size corresponds with my computer, whether or not a graphics card might fit, so, if you could help me out and maybe widen my knowledge on computers a little, that'd be great!

Cheers,

Henry