Help trying to set up an Ubuntu server as a router w/ a failover interface...

I have an Ubuntu server with two network interfaces - an ethernet and a WiFi network let's call eth0 and wlan0. So far I've been able to set it up as a router by enabling packet forwarding and then doing some iptables trickery. These are my iptable commands:

iptables -t nat -A POSTROUTING -o eth0 -j MASQUERADE
iptables -A FORWARD -i eth0 -o eth0 -j ACCEPT
iptables -A FORWARD -i eth0 -o eth0 -m state --state RELATED,ESTABLISHED -j ACCEPT

If I'm understanding correctly, the first command says "if you receive packets from a device, do NAT and then forward them with your IP", the second one says to forward packets from eth0 to eth0, and the last line says "if you get packets back, only accept them if a connection has already been previously established". This Ubuntu server is connected to a router which is connected to a modem that actually has internet access. I've set it up so that my router uses my Ubuntu server as the default gateway during DHCP requests. This works fine, I'm able to use devices to connect to the internet, and if I do a trace route, it first goes to the Ubuntu server, then to the router, then out into the great beyond.

Now, I've run:

iptables -D FORWARD -i eth0 -o eth0 -j ACCEPT
iptables -A FORWARD -i eth0 -o wlan0 -j ACCEPT
iptables -A FORWARD -i wlan0 -o eth0 -m state --state RELATED,ESTABLISHED -j ACCEPT

Which, if I'm understanding correctly, should forward packets through to the WiFi interface instead, but it isn't working. I'm still able to access other devices on the network but not the open internet. I also tried doing iptables -t nat -A POSTROUTING -o wlan0 -j MASQUERADE which as far as I can tell is unnecessary, but that didn't do anything. When I do trace route this time, it is able to get to the Ubuntu server but no further. I've also tried doing iptables -L -v but neither the wlan0 -> eth0 rule or the reverse have any packet count. I also tried doing iptables -A FORWARD -i lan0 -o wlan0 -j LOG --log-prefix "FORWARD: " to just log it first, but nothing shows up in /var/log/syslog even if I try to connect to the internet from a device.

I'm at a loss here so any help even debugging or if I'm going about this wrong would be greatly appreciated. My ultimate goal is to set up a failover so that if the LAN interface doesn't have a connection, it'll start sending packets through the WiFi interface which will be connected to a different internet connection.