Within the same generation (e.g. the HD6000 series mentioned here), you don't want to go with a lower model # card if gaming performance is what you're after. You don't want to go under the 6700 series as the rest of the cards are considerably slower. The memory size really doesn't matter seeing as how almost all modern mainstream cards feature 1GB minimum, and anything with 512MB isn't a viable gaming card. The reason you'll see some lower model # cards with fairly large amounts of RAM is because they need checklist features, it's just marketing.
If you plan on buying anything above the HD6800 series, you have nothing to worry about when it comes to specs, however, if you plan on getting an HD6750/6770, there is one area of concern: memory type. Some cheaper models of these cards come with significantly slower DDR3 instead of GDDR5. Just make sure to get the GDDR5 variant if you happen to pick one of these cards, and you'll be set.
