Is the existing network wireless G or wireless N? N will give you better range and faster speeds within 300-400 feet of the access point.
I seriously looked at Ubiquiti to have multiple access points that seemlessly integrate due to price point and POE capabilities. POE will limit the Cat5/Cat6 to 100Mbit, but that's not a concern much for wireless considering most G connections will only get 15-20Mbit actual performance and N only exceeds 100Mbit with line of site and close proximity.
http://www.amazon.com/Ubiquiti-Netwo...words=ubiquiti
It's best if you have wifi hotspots that are aware of each other because clients can pass between them.
In the case of using a second router, you'll need to put it on a different channel than the first, use a different SSID, and be aware that the WAN-port firewall can cause a lot of problems because you're dealing with a NAT'd network within a NAT'd network.
If you're able to totally disable the firewall features of the second router and only use it as an AP, you'll be better off. You can try turning off DHCP on the second router and see if you are able to get an IP from the first. The problem comes from the way the routing tables in most stock routers work. They try to make traffic flow through the WAN port to the LAN and WLAN.