You could look into MOCA adapters if the house has existing coaxial cable installed through walls for an old cable TV system. Plug an extra access point or two in and connect back to your main router via a few sets of adapters. It can cost a bit up front but it’s pretty reliable and if you buy old used 2.0 models you can save some money. (Just make sure they’re the same manufacturer)

Otherwise your options would be power line adapters to access points (bad, lots of chance for interference, neighbors adding a heavy appliance could break it).

Or nicer extending units located more closely together though if your walls are masonry or brick that may not help.

Also, inelegant and I hate to mention it but you could buy long, flat Ethernet cables, run them along the baseboards with the special retaining staples and connect that way to access points, though it does require space of a few cm door clearance in every doorway it has to traverse. Also flat cables technically violate Ethernet spec for preventing interference but in most single family homes interfere isn’t a big issue away from power supplies and runs so it would probably be okayish.

I’ve personally had very good results with Ubiquiti Unifi kit. It’s business grade, so not cheap, but highly effective.

The access points prefer to be wired, but have a fall back mesh mode. It doesn’t add much latency, or lose much bandwidth. Furthermore, the access points seem to have FAR better range performance than most home kit. I had a situation where a “long range gaming” access point became unreliable after about 10m. The Unifi LR gets over 50m in the same environment.

Network over Power line adapters can also be useful, and can reduce the number of access points you need.

Yes, I have experience.

Many years ago I helped a huge old house. They had the best success with powerline. At the time Mesh wasn’t available.

Nowadays, Mesh has higher bandwidth.

For Mesh, the signals travel through the air and through thin doors and thin walls. If there is something like a hall, stairwell or inner courtyard connecting most of the rooms, then placing the Mesh routers strategically around the hall will be your best bet.

For example, I placed the main router on the ground near the stairwell and the satellite at the end the stairwell where it could service two floors.

The routers could nearly “see” each other through the doorframes and from every corner in the house one router could always be “seen”

If the house is built more like a bunker or maze, then powerline will be your best bet.

In case you go for the powerline route, it will help to know a little how the cables run. Shorter, direct cables are better. One good option might be to place the internet router near the main breaker.

I use OpenWRT in a dual band router. Connect to my ISP with the 5GHz band, then create an access point with the 2.4 GHz band.

Mesh is terrible, don’t fall for it. It can get you at least some connectivity in the extended areas but it won’t be good connectivity.

The only actually good way to extend WiFi is to install access points and run cables to them.

Cables don’t necessarily need to be regular ethernet but that’s usually the best option. MOCA usually also works great. Powerline can be hit or miss, I’d only consider it a last resort and even then wouldn’t expect it to work well.