Just to add to the conversation, as mentioned, the current standard, 802.11n is considerably better than it's predecessors in both range, speed and security. That said the iPad employs 802.11g architecture (fully compatible with 802.11n) but favors WPA or WPA2 security for a stable and secure connection, something that may not be available in older Wi-Fi routers (which generally only offer the older and not-very-secure WEP protocol).
The Apple Airport Express Gabriel recommended earlier is a good option. We have FiOS broadband and the Wi-Fi modem/router supplied by our ISP is in bridge mode so that I can utilize both an Apple Airport Extreme and an Apple Airport Time Capsule (which is basically an Airport Extreme with a built-in hard drive) in our house. Apple's Airport Extreme is pricer than standard Wi-Fi routers, but both it and the Time Capsule required almost no setup, no maintenance and work phenomenally well with our iPad and all of our "iDevices".