Sirs,
just a few points to summarize the discussion
1. Your Internet speed will not increase with the use of a Gigabit Ethernet or wireless-N capable router
2. Internet bandwidth is normally a lot less than your LAN speed
3. LAN speed depends on your infra connection, theoretically these are as follows: 54Mbps - wireless-G; 300Mbps - wireless-N; 100Mbps-wired Fast Ethernet; and 1000Mbps-wired Gigabit Ethernet
4. Benefits of upgrading to wireless-N over wireless-G: besides the higher speed, wireless-N offers a wider range ... if you have a big house, multiple floors - wireless-N is the way to go
5. Generally, benefits of the faster LAN is really what the acronym implies > local area network only ...this is very useful if you have an NMT and you do not want the hassle of plugging-in your NMT to your computer everytime you transfer files > transfer speed is really much faster on Gigabit or wireless-N