In this review: http://www.legitreviews.com/article/1665/13/ They test the G620 with integrated graphics (much less powerful than any of the graphics cards you've listed) and the G620 really struggles and is obviously bottlenecking the integrated GPU.
If you're interested in playing modern games with half decent settings then I'd recommend upgrading the CPU aswell.
They test the on-board GPU but also test with a HD6850, In some tests the G620 does bottleneck quite badly compared to other higher end CPU's so I would personally go for a HD6770 or HD6850, anything more powerful will be partly wasted in some games.
I would opt for the Antec Neo as it seems to be a good quality unit for the price, though all the units you've listed are pretty good to be honest.
with regards to the GPU brand, its really down to your preferences, some brands offer a longer warranty, some come with more accessories or a better heatsink and fan design, and of course the price varies. So you have to decide what matters to you, narrow down your list of options and then look at reviews
p.s. what brand should i buy.
should i wait for the 660 ti and see if the prices drop on a 560 ti
i also dont live in america so dont give me sales.
thanks in advance
The HD 6850 is easily the best out of the three that you mentioned (HD 6850, HD 7770, GTX 550 Ti)
The HD 7770 and the GTX 550Ti are about the same when it comes to real world performance. The HD 7770 has been known to run better in more cases than the GTX 550Ti, but it also depends on the game and the setup. Sometimes the GTX 550Ti runs better, sometimes the HD 7770 runs better. The HD 7770 is about $15-$25 more than the GTX 550Ti where I live.