I have setup computers with similar cards (4670 512mb DDR3) and they game pretty good up to 1650x1080, even in older pre-phenom dual core AMD rigs. But those ones had fans. make sure you have some sort of airflow in your case for this one.
1GB is a waste on a 4670. Get the 512MB version on Newegg that I saw for like $36 USD after mail-in rebate... You can get an HD 4850 for $100.
What he said. If your PSU is weak though, the 4670 is attractive, as it is powered entirely off the Mobo, and is rather stingy with it use of electricity. With that CPU you could definitely get a lot more game for your buck with a 4850, provided your PSU isn't a dodgy low power no name brand unit.
Anti-aliasing is a higher-end graphical setting that sharpens edges.
Your machine is great, with the lowest part being the graphics card. If I were in your situation, I would save up money to buy a higher-end card, therefore eliminating the need to upgrade for the next year or so.