If not being used for games all of the cards would be over kill. All the cards you listed are high end "gaming" cards. The 670 being the newest out of your choices and offers great performance for the price so it gets my recommendation, but if you're not gaming, you could get a MUCH cheaper card and be perfectly happy.
you don't need such high end cards my brother does the same work on the same software with a 560Ti rather get such a card and use the saved funds to get a better cpu they do also play a huge part in editing work tough the i7 you have chosen is sufficient you can never have enough cpu processing power
The GeForce GTX 580 is certified for CS5 and drivers have been optimized thoroughly so I would choose the 580. This isn't for games so you pick what is certified. EVGA makes good cards. The Gainward you linked will be quieter, if that is a consideration.
If she does this for a living consider the i7-3930K on a 2011 socket motherboard with 16GB of memory. For the $400 extra it will pay for itself. If that's not in budget go with 16GB of memory, Premiere Pro will use it and RAM is cheap.
Okay Thank you everybody for your input and advice.
Im pretty sure i will go for the GTX580 as it is certified by Adobe and dont want to be messing about with"hacks" and stuff as it is for professional use.
I was also thinking about getting 16GB and you have made my mind up for me haha.
Im lead to believe she Render/Transcodes fairly big files in HD should I get a 3GB card or would a 1.5GB one be good enough?
If she is doing 4k edits go with the 3GB one. The 1.5GB one should be good enough though. If prices are fairly close then of course it can't hurt to get the 3GB model since some things you can do with Premiere Pro will use it. I would lean towards the 3GB model.