You should be able to just switch out the 3COM with a new wireless router.
Make sure to power cycle the modem after connecting a new router.
newer routers have a faster WAN connection which could even increase your internet speed on your network.
your current router has a 10Mb WAN and a 10/100 LAN ports.
newer routers have a 10/100 or 10/100/1000 Mb WAN and 10/100 or 10/100/1000 Mb LAN ports respectively.
You could also add a router, configured as an Access Point, to your network by connecting a network cable to one of the LAN ports of the wireless router
I like to use the WPA2 wireless mode over WEP.
A Linksys E2000 is a good, easy to configure router.