I'd aim for a wireless-g network adapter.
http://www.actiontec.com/support/broadband/gt704-wg.html#minreq

* * * * *
http://support.gateway.com/s/Mobile/Gateway/600YGR/3501243nv.shtml
http://support.gateway.com/s/Mobile/Gateway/600YGR/3501243sp2.shtml

According to the computer's specifications, it looks like you have three options for adding a wireless-g card:

mini-PCI card adapter(internal)
PCMCIA card adapter
USB adapter adapter

A wireless-g mini-PCI card would be my first choice. It might give you the best range, and you wouldn't have an external device that you can lose. Check with gateway to see if there is a recommended card:
https://support.gateway.com/support/copilot/chat_sales.shtml?id=400010

There are many wireless-g PC Card/PCMCIA adapters and USB adapters in the stores. You may want to avoid USB adapters if you need to use the ports for other things. Also note that you have USB 1.1 ports (not 2.0), and some wireless adapters work best on USB 2.0 ports.