If you're just getting in as a consumer, a $1000 VR-capable PC is going to age very quickly. In my experience, the only way to get any sort of legs out of a high-end purchase is to buy the top of the line. Unless you're buying right before a major product release, my experience has been that you end up spending less year over year than if you try to commoditize.
But I took the person I was replying to to be asking about getting in as a developer, considering the blog post is about getting in as a developer, and considering this site is full of developers. $2000 has been very consistently the price one pays for "top of the line PC with parts that aren't going to shit the bed". You should not cheap out on a development PC for VR. You're going to be doing a lot of experimenting and running up against performance limits during development. You should have some headroom to avoid giving yourself a headache for the day.
But go ahead. Buy a Radeon GPU. Have fun not being able to use your VR headset right before a crucial demo because of some obscure driver issue. Cheap out on a crappy power supply. See how many investors you get for our VR startup when your demo PC won't even start.
My personal experience has been that my VR development PC, which cost me around $1200 in the fall, has been great. I opted for parts just below the top of the line because I thought that would be the sweet spot. (I opted for a GTX 1070 rather than a 1080 for example). I have had no issues so far, but perhaps over the longer term I'll wish I had opted for the top of the line build. That is not the case yet. I see your point about buying for the long term savings rather than needing to upgrade every year. I haven't yet had issues with that but that may be true over a longer period of time.
Additionally, if you choose to buy a PC prebuilt rather than building it yourself it costs a lot more so your price range becomes more accurate than my estimates. That said if I were to give a cost estimate to someone who wanted to get a PC for VR development I'd tell them they can build a PC that can run everything for around $1200 USD and it would be completely adequate for development work for at least a year or two. As someone pointed out above that doesn't include the headsets, so the whole endeavour is still quite expensive.
If you're looking to get into high-end, room-scale VR with hand-tracked controllers and high-fidelity graphics, then yes. You need a Windows 10 PC with as much RAM, CPU, and GPU as you can muster. Plan on spending at least USD 2000 on a custom-built PC.
If you're looking to get into smartphone-based AR, you can use practically anything to write the code, and there are plenty of tools to be able to build completely cross-platform apps. But you will want a flagship phone, whether that's the latest iPhone or one of the Androids with a powerful CPU and GPU. AR is very CPU intensive. While there have been demonstrations of SLAM on GPUs, all of the implementations I'm aware of are doing it on the CPU.
Where should you start? Well, without hand-tracking of some kind, I don't really consider it VR. Google Cardboard, Google Daydream, Samsung Gear VR, and Oculus Rift without the Touch controllers are all glorified 2D interfaces. They don't provide anything actually new in terms of being able to interact with the application.
Smartphone-based AR apps will probably reach a wider audience sooner than VR. But if Microsoft's approach to headsets and Windows Holographic pays off, I think that is not a perpetual state of affairs. Ideally, this gets down to the size of a pair of sunglasses (which is very nearly the case already). At that point, smartphone-based AR is going to be a quaint novelty.