Will this graphics card work well for cycles? I'm considering buying the GeForce GT 610 2048MB on Amazon for $42.99.

Does this card work well for cycles? Is there a better alternative in the same price range? I want a basic graphics card that will speed up my occasional renders - nothing terribly fancy.
Absolutely! Although with only 48 CUDA cores, it might be rather slow... A slightly better one might be this one:
MSI GeForce GTX 710