NIC = Network Interface Card, another term for Ethernet card. What model number is your Linksys router? My guess is that since it seems somewhat older (supports only wifi G) it probably doesn't include gigabit Ethernet so the regular 100MB Ethernet is all you need for whatever card you get.
Something like this should be OK for you: FRYS.com¬*|¬*D-Link
Notice how it states it's a 10/100? That's the 2 link speeds it supports 10 and 100MB. If it was a gigabit card it would be listed as 10/100/1000 meaning it supports 3 link speeds 10, 100 and 1000MB. 1000MB = 1 Gigabit.