Yes it will help to have the N speed adapter,and that's a nice choice.
Given your usage, I don't see any obvious need to upgrade, not if it's working ok. Most of the time your ISP doesn't even come close to saturating your wireless network, G or N, so unless you have a need for a lot of local file transfers, I'd leave well enough alone. In fact, nothing beats a wired connection for gaming due to the higher reliability and lower latency. But of course that's not always practical.