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Building your own good-performance local network is simple. You need OpenWrt and, depending on the area you want to cover, a few really cheap routers.
Despite anything manufacturers are telling you, in a Middle-European house with brick walls and plenty of electrical lines and water pipes running through the walls your 100mW signal power router is not going to have very long range. Expect something in the 5 to 10m ballpark to get a signal better than -70dBm with 2.4GHz, 5GHz is going to be worse. Outside it's a different story, mostly depending on how clear your line of sight is and how many other devices are occupying the WLAN frequencies. If you live in a city, like I do, it gets pretty crowded fast. For example, my gateway router can see about 70 SSIDs in the area, luckily a good half of them squat on channel 11. (Dudes, we are in Europe, we can use 13 channels in the 2.4GHz band.)
Take a look how large your area is and how many levels you have to cover. I, for example, have an area of about 300m² to cover and about 70m² of them are a house with three stories. The top level is a roof, so it's actually not that big area-wise but for our calculation that's not important. This way I get a volume of 10m * 7m * (3 * 2,5m) = 525m³. Assuming that a WLAN router is roughly able to cover a box (obviously this should be a sphere but precision is not that important here) of 125m³ to 1000m³, I can see that I would in the worst case need about 4 routers to cover my house alone. There are other considerations to placement than optimal illumination, so I placed the gateway router close to my inbound WAN. From there I measured the quality of the connection using free and open source scanner software on a laptop to observe signal strength. Once signal strength dropped below -65dBm I placed another router where I had a structured cabling outlet. Turns out due to the shape of my house — an L — I only needed three routers. One roughly in the center of level 0 and level 2, one out in the small part of the L on level 1. I used the 4th to cover the garden, but that's a different story.
I assume you are using routers that run OpenWrt [1]. Set up the first router as if it would be a standalone device. You can configure the router via SSH or the webinterface [2]. The out-of-the-box configuration is fine, but by default OpenWrt does not configure WLAN and SSIDs. Using the webinterface (it is called LuCi) go to Network -> Wireless and at least set up a 2.4GHz SSID. If in doubt, consult the user guide.
[1] If you are starting with OpenWrt for the first time, I can recommend Cudy products.
[2] The OpenWrt user guide. Very detailed, sometimes esoteric.
I assume all your additional APs are connected to a cabled network in your home that is connected to the gateway router. BTW, this connection is called "backhaul". Wired backhaul is the best situation. If you have to use a wireless backhaul, we are actually talking mesh. That's a different story, too. I'll write it later. Back to the wired backhaul AP. Besides the router you are going to need a computer, too. I'll give you a quick step-by-step walkthrough:
1. Connect the computer to the future AP.
2. Set a hostname for the AP (physical location is good, eg. roof)
3. Set a password
4. Deactivate the services firewall, dnsmasq, and odhcpd
5. Disconnect the computer from the future AP
6. Connect the computer to the gateway router
7. Connect the WAN port of the future AP to a LAN port of the gateway router
8. Find the IP of the AP in the gateway router's DHCP leases list
9. Connect to the IP of the AP via web or SSH
10. Switch the AP's LAN interface to "dhcp client"
11. Deactivate the DHCP service for the LAN interface
12. Deactivate IPv6 for the LAN interface
13. Save & Apply
14. Logout
15. Move the cable from the WAN port of the AP to a LAN port
16. Receive new IP address from the gateway router
17. If you like set a static lease for the AP
18. Reboot AP
19. Done
If you want to enable fast roaming (802.11r) — and you should want that — see my earlier post [3]. It's somewhere at the end.