If you want something similar in speed for CUDA compared to the GTX580, you should choose at least GTX 1060, 6GB vRAM version (it also comes with 3GB vRAM version, which you should not buy)
You read here (English at the end):
Clément recommends as much vRAM as possible for Eevee (for CUDA the same is also recommended). Therefore you should at least choose starting from GTX 1050 Ti 4GB vRAM (You make sure that it is 1050 with “Ti” word in model). I am not sure if there are Out of Memory errors with Eevee/OpenGL, but perhaps little vRAM could influence speed/fps.
By the way, supposedly next month nVidia launches new cards, you should wait before buying.