Which should I choose 5670 1Gb or 512 MB?

I can assure you that buying the 1gb version will have no effect on performance at all. The only way you would benefit from having that amount of memory on that card is if you wanted to use if for eyefinity, you will not even use half of that vram gaming at that resolution mate, just go for the duel slot version if you can though, better cooling  

I will able to play for example GTA IV in high, won't I?
Thank you

No sorry, GTA IV needs a quad core processor to be played at high settings at a decent frame rate I am afraid (the game is badly ported), and also the card that you are buying is a med/low mainstream video card you should not expect miracles.

here is a video with someone with a fairly similar system to yours playing GTA IV on high settings getting 26 - 35 fps playing at 1280 x 1200.

http://www.youtube.com/watch?v=ejQAUZEvGCE

I guess it depends if you want to play it on high with decent frame rates.

the one with 512MB memory should be fine with you but don't expect too much out of it. as many other people said the game is poorly ported for pc. i've still remember even GTX285 (1GB ver) having hard time to max out the game

Ok, i think i chose a bad example. Will I be able to play fallout 3 in full resolution and a good quality?

yeh I would say medium to high at your resolution  

5670 1 gig vs 512 meg... only a handful of title will even utilise the greater amount of ram and unless you can find the 1 gig withing about 5 bucks of a 512 i wouldn't spend the extrra case on it


http://www.legitreviews.com/article/1187/15/

as for fallout 3 it was covered in the official tom's review of the card and should be fine

http://www.tomshardware.com/reviews/radeon-hd-5670,2533...

the 5670 will do great on fallout 3 however it might be cpu limited in your case