The router will never run faster than the internet you pay for. So if you only pay for 450m a gigabit router will still run the same speed.
Games use almost no bandwidth at all. Many are 300-500 KILO bits/sec, So you already have massively more bandwidth than a game uses.
Network performance in games is more about the quality of the connection rather than the size. You of course need to not be on wifi since that is one of the major causes of lag spikes in games. Leave a constant ping run in a back ground window to some ip like 8.8.8.8 and see if you get very large changes in the latency.
A general note on router performance. Even very inexpensive routers can pass 1gbit of traffic. You would only need a very...