What is this router's status regarding OpenWRT?

Bought this router today specifically as a guinea pig for my OpenWRT fun (wanna port some stuff over), and it was listed here http://wiki.openwrt.org/ru/toh/start as "Supported".
Then, on the page it was written off as "Partially" supported, indicating some issues with wireless. It's unpleasant, but I can live with that.

Tried to build an image for it, and now I have the following images in bin/:

openwrt-bcm53xx-asus-rt-ac56u-squashfs.trx
openwrt-bcm53xx-asus-rt-ac68u-squashfs.trx
openwrt-bcm53xx-asus-rt-ac87u-squashfs.trx
openwrt-bcm53xx-asus-rt-n18u-squashfs.trx
openwrt-bcm53xx-buffalo-wxr-1900dhp-squashfs.trx
openwrt-bcm53xx-buffalo-wzr-1750dhp-squashfs.trx
openwrt-bcm53xx-buffalo-wzr-600dhp2-squashfs.trx
openwrt-bcm53xx-buffalo-wzr-900dhp-squashfs.trx
openwrt-bcm53xx-netgear-r6250-squashfs.chk
openwrt-bcm53xx-netgear-r6300-v2-squashfs.chk
openwrt-bcm53xx-netgear-r8000-squashfs.chk
openwrt-bcm53xx-smartrg-sr400ac-squashfs.trx

None of them seem to correspond to my router. Which one should I flash?
Or, how do I build one specifically for my piece?

Maybe you'll read description of CONFIG_TARGET_bcm53xx you decided to use?

And, what exactly do I find there?

"Broadcom BCM47xx/53xx (ARM): Build firmware images for Broadcom based BCM47xx/53xx routers with ARM CPU, *not* MIPS."

Well, yeah. What now?

The other one with similar caption (CONFIG_TARGET_brcm47xx, Broadcom BCM47xx/53xx (MIPS)) gives me unsurprisingly 47xx files. Not one of them is for my device, although there's one generic. But I believe I shouldn't flash a firmware for wrong architecture.

Sorry to tell you, but your model (Asus RT-N10U) is listed here:
  http://wiki.openwrt.org/toh/possible
...as "possible", not "supported":
  http://wiki.openwrt.org/toh/start

We are working on the ToH, but it is a big job to get everything up to date and to make it easier to use.
I find it particularly confusing that the current ToH is distributed over 5 pages. For this reason, we work with a temporary single table:
  https://dl.dropboxusercontent.com/u/906 … index.html

The ToH indicates that target=brcm47xx.
The device page indicates it is a mips 74K cpu:
  http://wiki.openwrt.org/toh/asus/rt-n10u

So this is probably where you should look for generic images, or find inspiration for building yourself:
  https://downloads.openwrt.org/snapshots/trunk/brcm47xx/

I suppose you are aware that flashing the wrong image may brick your router. The "possible" status is not a very well supported one. But any findings, success or failures you encounter, you are very welcome to post it here or update the device page.