That CPU is most likely also going to bottleneck you somewhat, it may be a 4t/8c CPU, but it's from 2009 and its single threaded performance is pretty bad for current times, around as powerful as one of the i7 900 series which at this point is definitely starting to show it's age for modern gaming. Adding another CPU in the second socket won't do much to help, since it's not going to magically make single threaded performance better, so you may be better off saving up for an entirely new PC instead to be perfectly honest.
As to minimum GPU required for VR, you can actually get away with using a GTX 970 still (so long as you don't mind low graphical settings for more intensive games, like Half Life Alyx), but I would 100% agree that a 1060 is probably the minimum you should go for.
As to cheap VR headset, to be honest now is probably not the time to go looking for a
cheap one, thanks to current demand even something cheap like WMR headsets are selling for way more than they're worth (like $300-$500+) so you're either going to need to spend some cash if you want any VR right now.
Although it seems Oculus right now are currently selling "refurbished" Oculus Rift CV1 kits for $300 right now on their own site, which is waaaay better than the $400 you're going to spend by going used on eBay.
https://www.oculus.com/rift/ <
