A computer that is well below their minimum spec will also run an Oculus without any problems. For instance, my DK2 ran perfectly on my i5-4590 with a GTX660 2G GPU (Fatal1ty H97 mobo, 16G DDR3 ram - built for NZ$900 (US$750) in 2014).
Once you get started in VR though, you'll definitely be playing other stuff, in which case I'd recommend getting a more powerful GPU, as the CV1 resolution and refresh rate is a bit higher than the DK2's. But don't buy a "package" - they charge premium prices for low-quality components in order to make as much profit as possible.