What will be your gaming resolution? Both GTX 570 or GTX 560ti are doing great @ 1080P, the HD 7870 is performing as powerful as a GTX 580 for $360, even the GTX 580 is sold in this price range but hard to find nowadays....
Second, you need to upgrade your PSU to at least a 550W quality branded one.
Agreed you need to post your resolution and expectations on what you want? Do you want the best card for 350 Euro or the cheapest card to can get a certain performance level out of?
I also agree that you'll typically need a minimum of 500W PSU. Might as well get some headroom if you are going to upgrade the PSU. If you want to stay with your current PSU, you might check in on the new generation cards from AMD and Nvidia since they consume much less power. The 7770 might be good enough for your needs and might work for your PSU, but I'd have to research to make sure. Do you know how many PCIE connectors you have?
There's no 1280P, the maximum resolution by your monitor is 1920 x 1080, it's called full HD 1080P. It's a very high resolution to view all the visual effects purely and clearly specially in gaming. Maybe you meant 1280 x 1024.
1080P requires a very strong GPU to play all the current games at highest resolution without feeling any lag.
Those what you should look at and pick the suitable to your budget.
GTX 580 / HD 7870
I think I'm getting lost in the currency conversion here as well. IF at 7870 is in your price range... it's a great card for the money and I'm getting two myself. You will be able to play all the games at excellent quality on one 1080p screen. Naturally, if you can afford the 680 it's obviously better, but may be overkill for 1920x1080p considering the price difference. You'll get better results of course, but IMO not worth the $150US difference. Same applies to the 7970, although the only reason I would pick up a more expensive 7970 over a 680 is if you plan on Crossfire and SLI isn't an option, or computational performance is a concern outside of gaming where Nvidia skimped out.
The reason I mentioned the 7770 is because it will most likely work with your current PSU and will save you money and you'll still have adaquate power for the current games on the market. I wouldn't even think about these other cards with your PSU.