In all likelihood, it's not the router that's the problem, at least not YOUR router as opposed to someone else's router, or a different brand of router.
The problem is two-fold. The internet is inherently a high latency environment. That’s what gives it its flexibility. Your data is broken into packets that are routed across the internet, having to compete w/ other traffic, filtered, prioritized, etc., and arrive at the other side, sometimes out of order, sometimes corrupted and requiring a resend, etc. It’s almost hard to believe it actually works when you know what’s happening under the covers.
But that same high latency wreaks havoc w/ certain applications, esp. those sensitive to response times, such as gaming and VOIP.
Now you compound the problem w/ wireless. Wireless is as bad as it gets for gaming and VOIP since all your transmissions are subject to possible interference, obstacles, etc. Plus, wireless is half-duplex. Only two wireless stations can be communicating at any given time. All other wireless stations must WAIT! And that kills both your throughout and response times. And that’s on a good wireless connection. Add some interference, multiple users all vying for the same wireless connection, and things can deteriorate quickly. You don’t normally notice it using your browser because you’re less sensitive to it. But that same lag in a game might mean the difference between virtual life and death!
So the bottom line is, avoid wireless if at all possible. Yes, it’s terribly convenient, but it’s just not a good solution when response time is critical. As far as the internet itself, there’s almost nothing you can do about it. It’s beyond your control. You just have to be a bit lucky to have an ISP and route from you to the gaming host that’s relatively responsive. And that can vary from moment to moment, hour to hour, or day to day.
I suppose it’s possible that wireless N being faster than wireless G could improve things a bit. But it all depends on how much of the current problem is due to environmental issues vs. the speed of the interface. I suspect it’s far more the former, and would dwarf any of the advantages of wireless N. But who knows. If you have interferences issues, wireless N using the 5GHz freq. might be worth the investment with its twenty-three non-overlapping channels and fewer users.