What used iMac model to buy, 27" 2010 or 2011

Updating video cards is a no-go for iMacs, since the video module is specific to the motherboard. The only Intel Macs that permit video upgrades are the aluminum Mac Pro towers (2006-2013), which have AGP and PCI-E slots. Even then, the card you install has to have an OSX driver.

I agree with mayer: You're much better off getting a 2011 iMac than a 2010, because the Mid 2011 model is the first generation with Thunderbolt ports. This makes the computer far more extensible, since you can attach all kinds of external devices (hard drives/drive arrays, giant monitors, FireWire/USB 3.0 gadgets) without the speed limitations of the onboard FireWire and USB 2.0 ports.

A lot of external drives now come with USB 3 interfaces, which are much faster than USB 2. Although the iMac didn't get onboard USB 3 ports until the Late 2012 generation, you can get USB 3 ports by using a Thunderbolt breakout box available from a variety of manufacturers including Akitio, Belkin, CalDigit, Matrox, and Sonnet. You can also get Thunderbolt drive housings, which can give you external storage nearly as fast as the internal drive - maybe faster, if you're using an external solid-state drive.

The video repair extension mayer links to in the 9to5 Mac article isn't currently posted on Apple's support site, but it may be an issue the Genius Bar addresses as affected computers show up. There is a different repair extension with failed 1TB hard drives, which applies to iMacs from October 2009-July 2011, so you should be aware of it.