It makes sense, but is it not better to have more firewalls to breach to protect your data? Or would a breach in the first firewall automatically open path through other firewalls in the LAN?
No, despite what you might have seen on TV (Battlestar Galactica and its 6 firewalls comes to mind ) having more is not better. In fact, running software firewalls on your internal devices isn't going to do much more than annoy you. The firewall/NAT on your router will keep you safe from 99.9999% of all internet based attacks.
I would be more concerned about the actions of your network users (clicking bad links to phishing attacks, downloading infected files, etc.) than I would about attacks from the internet. No amount of sophisticated firewalling will prevent the actions of idiot users. Trust me, I know this for a fact.
I'm just glad you got it to work! I hate setting up wireless networks and stick to wired (I have very well hidden ethernet cables running through my house!)
And my personal preference on Firewalls is just have the one on the router like severusx says - no need for additional firewalls!
Definitely port-forward any applications you use through the router! And never use a DMZ... even for gaming!
For your router, there is a guide here on how to access the router to do some portforwarding: pcwintech.com/port-forwarding-tp-link-tl-mr3420-tp-link-firmware
Also here is a list of Application/Game Ports (including PSN): portforward.com/cports.htm