Dedicated pc for VR room

[invaderSnarf]

Budget (including currency): either $400-600 or ~$2000

Country: USA

Games, programs or workloads that it will be used for: Run a valve index and play VR games, specifically Hotdogs Horseshoes and Hand Grenades with mods

Other details 

I recently moved into a house and have a room for VR now. The problem is, my primary PC is in a different room where I stream and play games. So I am looking at building a dedicated pc for VR for this other room. 

 

My current GPU is a 2080ti. My initial plan was to upgrade that card to something better and use it in the VR rig, but looking at what would be a decent upgrade from my 2080 that is still going strong seems not at all budget friendly. My second plan is get a cheaper GPU (was thinking maybe a 1660 or go as far as a 3060). Would it be worth waiting and upgrading my 2080ti and using it for VR, or would it be better to go for a lower value GPU for VR?

 

The other parts of the pc would be either a Ryzen 5 5600 or intel i5-12gen with 16gb of ram with appropriate motherboard and small form factor case to fit it all in so a relatively budget PC.