Ubiquiti - UniFi Dream Wall (UDW)

Run Cat6 not CCA to every room, 3-4 cables for APs to do POE, 3-4 Ubiquiti APs, and then you can use a Ubiquiti Dream Wall (UDW) which is a router/POE switch/AP all in one. You can buy an additional power supply for the UDW for redundant power and place the UDW in one of the AP spots centrally located in order to reduce the cable length to each location. Mount your APs to the ceiling in their respective locations and POE them with the UDW. Ubiquiti also has a site survey tool, WiFiman, as well as a floorplan tool to assist you in AP placement for best coverage estimate. I would make sure to put your UDW on a UPS so that you have that protection as well as uptime. When you run your Cat6 make sure you pull a pull wire through with it for possible future use.

I have two U7 Wall and a U7 Pro, reliability is ok but range with concrete walls is just absurd. Besides that I like the system a lot.

Moved from ASUS to Unifi. Reasonably low end kit for them, over 50 devices. Works like a dream. Even the Wi-Fi mesh.

UniFi, hands down. I don't know what you consider "similar nonsense", - prosumer and a lot of business will use a controller that manages the configurations and statistics. The Cloud Key is a somewhat older implementation of the UniFi setup where it performed as the controller and an NVR for cameras. They've split that off - you can get gateways (router/controller) that does not have the video incorporated any longer. The "cloud" in some of their hardware doesn't mean it's run from the cloud or whatever, it's simply part of the model name. You can run it all standalone without being tied to their servers (though it's pretty convenient at times). Similarly, they have "mesh" in the name of some of their APs - but all of them can be wirelessly uplinked. It's a matter of them associating through marketing to the massive consumer "mesh" marketing. But it's still prosumer stuff and uses the same controller as the rest. My favorite feature is reliability. It's been rock solid for me through 6 years (I've moved through three upgrades and it's just stable. I love it. Look at the Dream Router 7, UniFi Express models, and Cloud Gateway models for some pretty darned good home solutions. The Dream Machines are great also, they are rack mount though and tilt towards having the video features. Should you choose one of the simpler offerings and want to go video later - there are standalone DVRs - including the Cloud Key+, which is still popular - that you can add. There is other prosumer gear, but Ubiquiti UniFi and TP-Link Omada are the only ones I know of with the unified management.

You could do one Asus router then run a cable across basement and do another Asus router in AI MESH mode. Or id setup Ubiquiti cloud gateway (any of the 3) and u7 lite then a cat 6 across basement to another u7 lite. You could test one nice asus router in the middle of the house basement or maybe the Ubiquiti Gateway with 1 U7 Pro or something in the middle and always have the option to add another of each too.

I am a fan of the Unifi Cloud Gateway series. Have the fiber version myself, which can also be used for UTP WAN. Not coax. 

For your setup Best signal: Unify Cloud Gateway Router, and U6+ or U7 Pro OR Simplest: UDR7 OR Lowest cost: Unify Express 7

Any Cloud Gateway from Ubiquiti paired with AP’s. Easy to setup and manage.

Asus Expert Router EBG19P seems to have some benefits over Ubiquiti Cloud Gateway, such as more ports. But it's hard to argue the awesomeness of Ubiquiti UI - I love my UDM Pro. Props to ASUS WRT (Merlin) too. Like others said, just turn off DHCP and WiFi on the ATT Gateway and let your router do the lifting. Couple with Asus Zen Wifi or TP-Link Deco mesh system in access point model for expandable, upgradeable wireless. Eero won't support this setup (no AP mode).

Since you have cable Internet and it runs into the basement, you hopefully have coaxial cables available to you throughout the house, and usually in key locations. Just look at the area where all the coax ends should meet, likely in the basement where your modem/router is at and plugged into. If you do find this bunch of coax, you can use it with MoCA Adapters to build a wired Ethernet network inside your home. If you can achieve that, then getting good WiFi everywhere will be easy, as well as providing wired capabilities for other devices in needed locations. MoCA Adapters can be a bit expensive, but worth the cost. If you can build this MoCA network, then whatever you choose as the router and Access Points will work very well, including a 3 pack of a reputable mesh brand. For mesh, I use and can recommend eero. But ASUS Zen mesh is also praised a lot, and has more configurability. If you want to go higher end, you can get an Ubiquiti Cloud Gateway router, a Ubiquiti PoE switch, and some Ubiquiti Access Points. It's more expensive, but very capable of advanced setups, and is very stable. I use Ubiquiti at another home and in my office location, and I can recommend them personally as well.