.... So I placed an Airport Extreme (via ethernet to the cable modem) between brickwall 1 and brickwall 2 and created a different wireless network.
There is no need for it to create a different wireless network. Since you are interested in the best alternative, that would be to have your Extreme create a network with the exact same name and security settings as the Arris router. That way you will have created a "roaming network" in which your wireless devices can wander from one wireless access point to another more or less seamlessly.
In addition, configure your devices capable of using the new Extreme's 5 GHz network to use it exclusively. That is the best alternative for avoiding wireless intereference, at the expense of reduced range due to interventing objects and structures. If your home is sufficiently distant from other competing wireless networks e.g. you have no neighbors, wireless interference is less of a concern.
As you suspect your home is rather large for only two access points. You would benefit from a third access point, connected the same way (via Ethernet, and configuring a roaming network).
The following KB articles explain how to create a roaming network:
If you need to extend the range of your wireless network, which method should you use?
For 802.11a/b/g/n Wi-Fi base stations:
- Roaming Network (Recommended)
- Wirelessly Extended Network
You might need to drill holes and fish wires through walls and ceilings, but it's worth the effort.
Couple a follow-up questions as I am fairly junior when it comes to networks.
Since the Comcast cable modem is also broadcasting a wifi signal, do I apply this network settings to the Airport Extreme? I am assuming if this is the case, then I opt for the "Bridge Mode". Correct? Also, can I use an Airport Express to the Extreme (via ethernet) to help with the wifi range? Thanks so much for your patience :-)
Since the Comcast cable modem is also broadcasting a wifi signal, do I apply this network settings to the Airport Extreme? I am assuming if this is the case, then I opt for the "Bridge Mode". Correct? Also, can I use an Airport Express to the Extreme (via ethernet) to help with the wifi range?
Yes, yes, and yes. Whatever wireless security settings you are using to connect to the Arris router (WPA2, for example) need to be exactly the same on every additional base station.
Configuring the Extreme to connect to the Internet "via Ethernet" will require that its "Connection sharing" be set to "Off (Bridge Mode)". The Comcast / Arris router should be the only device configured to "share an IP address".
You can certainly use an Express as an additional base station. Not knowing your exact environment I cannot be 100% certain but from what you describe I think it would be ideal for your needs.
Use these same "connection sharing" and wireless security settings for the Express.