802.11g has a nominal data transfer speed of 54Mbps which, in practice, is likely to be closer to 30Mbps. This will generally be faster than your internet connection, unless you're on something like Virgin's 50Mbps Cable service. Therefore, for the internet "G" is probably fast enough.
Where a faster connection will be beneficial is if you are likely to be transferring large files between computers in a local network. Wired ethernet runs at 100Mbps (or Gigabit at 1000Mbps) and, depending on the hardware, 802.11n wireless will have a nominal speed of 150Mbps or 300Mbps.