It also depends on what resolution and what graphic settings you want to use. In general, for anyone who wants to play games the minimum card should be the Radeon HD 7750. To me that is the most basic card to buy for a relatively low price of around $90 - $100 for the DDR5 version. It more or less equal to the Radeon HD 6770.
The more performance you want to more you need to spend.