You can go really cheap: AMD 8300+$40 mobo/stock cooler +500w psu + gtx 970 + generic mouse/keyboard/monitor + $30 case + 8GB ram + $20 SSD and come out around ~$600.
For an upgradeable Intel solution with a decent SSD/HDD, 16GB of ram, huge case, and a hybrid water cooler: ~$945.
In my situation, I bought a 980ti, Corsair 750w PSU, GPU/CPU hybrid coolers, and new case. It was around ~950, but my older 2600k is keeping up with the times. I'm also doing neural networks/Vive game dev. I really wanted to wait for Nvidia to relase their Pascal line before buying a video card.
That makes my jump into VR/AI cost around 2k (~1000 PC components, ~900 Vive). Yet, a long awaited upgrade. My 4850 video card is from 2008 and could still play current games in lower settings/resolutions.
Side bar: because my GPU wasn't a reference board the hybrid cooler would not mount. I had to hacksaw my brand new card's heatsink and zip tie the fan back to it for the VRM/ram cooling. Anxiety was an understatement. Luckily, the 980ti idles at 75F now and maxes at 120F (from idle 120F/max 180F).