Try this first before you spend money on new equipment. Turn off DHCP in the wireless router. Connect the wireless router to the Gateway/router (ethernet-to-ethernet). Your computers will pick-up IP addresses from the Gateway/router DHCP server as you stated above. Hope this help.
I currently have a cable modem that's connected to a Belkin DSL/Cable gateway/router that acts as a DHCP server with the subnet 192.168.2.x. My desktop computer is connected directly the gateway/router. I have a Netgear wireless router (MR814) connected to the gateway that dishes out an IP address to my notebook computer on the subnet 192.168.1.X. Theoretically, things work fine.
In reality the MR814 is terrible. It regularly drops the IP assigned by the gateway/router and loses connection to the Internet. I've tried static IPs, I've tried connecting the MR814 directly to the modem, and nothing fixes the problem. It continues to drop the IP and it takes several physical reboots to force it to get a new IP. The notebook keeps its connection to the router but it's useless if the router keeps disconnecting from the Internet.
Long story short, I want to get a new router that isn't awful but should I get an access point or a router? I want the wired computer and the wireless notebook to be on the subnet, but can't I just plug the wired computer into one of the ethernet points in the back of the wireless router?
In other words it would look like this:
Internet-->Cable Modem-->Gateway-->Wireless Router-->wired desktop & wireless notebook
Or am I missing something here? Also, I was using the gateway for security. Am I kidding myself by including it in the above scenario or is really adding another level of protection to my home network?