If you plan on maxing out titles no. Streaming is handled on the CPU, so it depends on the chip you have. I would go with a 27" if you sit further away, but the bigger the screen, the more expensive it is. You also want a good one with a good refresh rate (144hz is the norm these days).
For maxing out games on 1440p, you want to look at the GTX 1070. If you don't mind turning down the quality, I suppose a GTX 1060 3GB wouldn't hurt, but then again, the 6GB version would perform better.