1GB is wasted on the HD 4560 because to slow to make use of it. 1GB is necessary once you game at 1920 x 1200 (1920 x 1080) which the HD 4560 is too weak to handle.
The least expensive card I would get is the HD 5670 for about $90 and is about 30% more powerful than the HD 4670.
Beneath that is the HD 5570 for $70 which is basically equal to the HD 4670 ($65).
Of course it all depends on what resolution you want to play at.