I need stability and reliability most of all. I'm willing to pay for quality.
I have a nominal 100 Mbps connection out here in the boonies, but usually get more than that.
I would probably use an external AP unless the device's onboard WiFi is superb; so either wired or wireless recommendations are appreciated.
At least one USB 3.x port is preferred (for onboard NAS), but I'd be willing to cough up the money to buy a freestanding NAS if an otherwise-superb device lacked USB.
I only need one WAN port and one LAN port because I run everything through a managed switch, but spare ports are always good to have.
The router will be on my right and I'm half-deaf in that ear, so I don't care about noise.
I have a preference for Intel, but I'm not married to them.
I'm interested in either manufactured devices or a parts list for something on, say, a mini-ITX board.
Any particular reason you are interested in a mini PC instead of a consumer router device? Given your bandwidth (100Mbps), pretty much any recent router will easily be able to handle the throughput, usually with lower power consumption than a mini PC (which admittedly isn't a huge draw). There are also devices that have onboard USB 3.0 ports, although I don't know how good the performance is for NAS functionality.
Since a "PC" can be made of pretty much any hardware combination, the OpenWrt x86 builds are kind of bare bones and most drivers are omitted. There is more up-front configuration necessary, too. Upgrading from one version of OpenWrt to the next (service releases and/or major version upgrades) are less straightforward, too. You can mitigate some of these complications if you build your own images (not difficult, but possibly involving a learning curve).
By contrast, each OpenWrt supported consumer router has a known hardware configuration and there are downloadable images with all required drivers and a default state that is essentially plug-and-play for many people. Upgrades are much easier, too. You may, of course, build your own images here, too, but it is not all that necessary in many cases.
Regarding the NAS, my personal recommendation would be to get a standalone NAS since you'll have better options when it comes to high performance purpose built hardware+software. This could be one you build with standard PC hardware or a true purpose built NAS. OpenWrt does have the ability to be used as a NAS, but it is not optimized for it and it requires a bit of extra work to run. I'm also a proponent of dedicated NAS devices in this scenario because your router is directly connected to the internet. This means that a misconfiguration of your router or other security risks could compromise both your router and your NAS in one shot. But, if you choose to go with your combined approach, the x86 option will likely give you better performance than a consumer router, but I'm not sure if the performance difference will matter (depending on your application).