Bottleneck is an easy misconception. Your CPU handles the game engine. The CPU is capable of a certain amount of FPS depending on the game engine code and how fast the CPU is. The GPU is going to handle resolution, pixel shading, post effects, ect, and depending on the resolution and settings, a GPU will be capable of certain FPS.
In summary: You pick your CPU depending on the game engine. You pick your GPU depending on the detail settings.
A lot of newer games will utilize more than two cores, so in especially those games your CPU will suffer. A vast majority of the existing catalog of all games only needs 1-2 CPU cores though, so your CPU will be fine for those.
I would get a more powerful GPU like the R9-270, and save up for a...