Best to get a GPU that meets the recommended specification

VR is way more demanding than single screen 1080p gaming at 60hz.
https://www.oculus.com/en-us/blog/powering-the-rift/
The default eye-target scale is something like 1.3 times the final display resolution. This is because the image has to be warped, to take account of the lenses, which then results in some of previously rendered image being discarded when it finally makes it to the displays. There are methods being developed to help with this, see the PR slides from Nvidia and AMD (foveated rendering is the tech), but best to play it safe for now.
Given the GTX 960 has around 2/3rds the horsepower of a GTX 970 you're a long way short. Frankly while the Oculus specs may be OK for titles being developed specifically for VR or ones that it will showcase in their store front, if you have your eye on modern AAA titles you'll want something a lot more powerful. Roll on Polaris and Pascal.