From the WAN port of the modem you connect to the wired router's internet port. Both the modem and the wired router should have DHCP enabled (the Modem is on your WAN side, and the wired router is on your LAN side). Your wireless router is plugged into one of the LAN ports of the first router no doubt and with DHCP disabled, you should not get any IP conflicts (you only have one laptop right, so where is the conflict?).
What is the IP of your wired router, this should be also the default gateway?