In most cases, G is enough to share the Internet. WiFi-G is rated at 54 Mbps; the average residential internet connection is less than 10 Mbps in many countries, including the USA.
However, file transfers between devices are noticeably slower on G than on N, which is often rated at 150 Mbps. Many N routers uses multiple connection (MIMO) technology to increase throughput even further.
So, it depends. Are you strictly sharing your home Internet connection, or do you transfer files or print wirelessly? If the latter, get N. If the former... well, get N anyway and futureproof your network.