Okay, I am uncertain how well Blender will be able to break the render job down into chunks that could or would fit into VRAM on GPU rendering, though obviously it is appropriate to be concerned about VRAM size restrictions.
The largest about of VRAM available on an Nvidia card that I can find on short notice is 24 GB:
http://pcpartpicker.com/product/fqmxFT/pny-video-card-vcqm600024gbpb
and that is well outside your listed budget.
Honestly, I do not think you would do much better than to get the system linked above by WhoBeThePlaya (2 x Xeon for 16c/32t). That would be a lot of CPU rendering power, and you would have no issues with RAM running 128 GB. It still might be slower than some GPU rendering on smaller scenes, but for anything pushing 30 GB I think you would be better off focusing on CPU rendering.
Maybe you could pick up a 1080 or Titan or something for smaller scenes later?