ZeroRequiem :
Oh I see you want to use Blender, well in that case Nvidia GPUs are a must. Im also modeling and rendering in blender (i7 4770k, R9 290 Tri-x), everything runs smoothly but you can do the whole rendering on Nvidia GPU-s a lot faster. Sadly its currently not supported to render scenes on AMD GPU-s.
Adobe thrives with Cuda, Blender support only Cuda

http://wiki.blender.org/index.php/OpenCL, Handbrake and Gimp have support for both (but quality suffers in GPU encoding in Handbrake) and not sure about DaVinci Resolve Lite... I was inclined towards OpenCL because it's unbiased and have an open platform available for all but stats are against it..