I brought up CPU because I've personally run the game on the lowest possible settings (including viewport scale) and managed to keep around 60 FPS on a shitty NVS 5400M, based on the GeForce 540M chip. However the CPU used was a mid-range mobile Ivy Bridge i5 and 8GB RAM.
Obviously you should upgrade both, but the CPU is the biggest bottleneck right now. You're going to want at least 4 threads if you want OW to start being GPU bottlenecked. For instance, a Sandy i3 handily beats the G3258 just because it has hyperthreading (dual core + HT).